LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIjpGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTA==JSFHThe most common way of evaluation expression numericly is using the command LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEmZXZhbGZGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn. There are several examples on the "Maple Introduction" chapter. You can find more information on the next link: evalfLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=Note, many of the information in this chapter is token from LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEoU3R1ZGVudEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRKlsyNTUsMCwwXUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2Jy1GIzYlLUYsNiZRMk51bWVyaWNhbEFuYWx5c2lzRidGL0YyRjVGMi9GNlEnbm9ybWFsRidGMkZALyUlb3BlbkdRIltGJy8lJmNsb3NlR1EiXUYnRjJGQA== package.
<Text-field style="Heading 1" layout="Heading 1">Algebric equations</Text-field>In this chapter we show few methods which Maple has and helps us to solve algebric equations numerically.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(); # input placeholder
<Text-field style="Heading 2" layout="Heading 2">Iterative method</Text-field>There are several Maple commands for the Iterative method. Here are the links to Maple help page for each command:Iterative ApproximateIterative FormulaIterative Formula TutorThe Iterative method learn on this course is trial and error method.JSFH
<Text-field style="Heading 2" layout="Heading 2">Newton method (Newton-Raphson)</Text-field>The Newton command numerically approximates the roots of an algebraic function, f, using the classical Newton-Raphson method.Newton(f, x=a, opts)Newton(f, a, opts)
f-algebraic; expression in the variable x representing a continuous functionx-name; the independent variable of fa-numeric; the initial approximate rootopts-(optional) equation(s) of the form keyword=value, where keyword is one of fixedpointiterator, functionoptions, lineoptions, maxiterations, output, pointoptions, showfunction, showlines, showpoints, showverticalline, stoppingcriterion, tickmarks, title, tolerance, verticallineoptions, view; the options for approximating the roots of f
All the options above are shown in the Options chapter at the end of Algebric equation chapter.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print(); # input 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print(); # input 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print(); # input placeholderJSFHJSFHJSFH
<Text-field style="Heading 2" layout="Heading 2">Secant method</Text-field>The Secant command numerically approximates the roots of an algebraic function, f, using a technique similar to Newton's method but without the need to evaluate the derivative of f.Secant(f, x=[a, b], opts)Secant(f, [a, b], opts)
f-algebraic; expression in the variable x representing a continuous functionx-name; the independent variable of fa-numeric; one of two initial approximates to the rootb-numeric; the other of the two initial approximates to the rootopts-(optional) equation(s) of the form keyword=value, where keyword is one of functionoptions, lineoptions, maxiterations, output, pointoptions, showfunction, showlines, showpoints, showverticallines, stoppingcriterion, tickmarks, title, tolerance, verticallineoptions, view; the options for approximating the roots of f
All the options above are shown in the Options chapter at the end of Algebric equation chapter.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print(); # input 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print(); # input 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print(); # input placeholderJSFHJSFHJSFH
<Text-field style="Heading 2" layout="Heading 2">FalsePosition method</Text-field>The FalsePosition command numerically approximates the roots of an algebraic function, f, using a technique similar to the Secant method, but bracketing is incorporated.FalsePosition(f, x=[a, b], opts)FalsePosition(f, [a, b], opts)
f-algebraic; expression in the variable x representing a continuous functionx-name; the independent variable of fa-numeric; one of two initial approximates to the rootb-numeric; the other of the two initial approximates to the rootopts-(optional) equation(s) of the form keyword=value, where keyword is one of functionoptions, lineoptions, maxiterations, output, pointoptions, showfunction, showlines, showpoints, showverticallines, stoppingcriterion, tickmarks, title, tolerance, verticallineoptions, view; the options for approximating the roots of f
All the options above are shown in the Options chapter at the end of Algebric equation chapter.JSFHNote, using this method you must choose 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 in the way that 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print(); # input 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(); # input 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print(); # input 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print(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=JSFHJSFH
<Text-field style="Heading 2" layout="Heading 2">Bi-section method</Text-field>The Bisection command numerically approximates the roots of an algebraic function, f, using a simple binary search algorithm.Bisection(f, x=[a, b], opts)Bisection(f, [a, b], opts)
f-algebraic; expression in the variable x representing a continuous functionx-name; the independent variable of fa-numeric; one of two initial approximates to the rootb-numeric; the other of the two initial approximates to the rootopts-(optional) equation(s) of the form keyword=value, where keyword is one of functionoptions, lineoptions, maxiterations, output, pointoptions, showfunction, showlines, showpoints, stoppingcriterion, tickmarks, title, tolerance, verticallineoptions, view; the options for approximating the roots of f
All the options above are shown in the Options chapter at the end of Algebric equation chapter.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=Note, using this method you must choose 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 in the way that LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYuLUkjbWlHRiQ2J1EiZkYnLyUnaXRhbGljR1EmZmFsc2VGJy8lK2JhY2tncm91bmRHUSxbMjU1LDI1NSwwXUYnLyUnb3BhcXVlR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JKG1mZW5jZWRHRiQ2Ji1GIzYoLUYsNidRImFGJ0YvRjJGNUY4RjJGNS8lK2V4ZWN1dGFibGVHRjEvJTBmb250X3N0eWxlX25hbWVHUSgyRH5NYXRoRidGOEYyRjVGOC1JI21vR0YkNi9RJyZzZG90O0YnRjJGNUY4LyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGZm5GKy1GPDYmLUYjNigtRiw2J1EiYkYnRi9GMkY1RjhGMkY1RkNGRUY4RjJGNUY4LUZJNi9RIjxGJ0YyRjVGOEZMRk5GUEZSRlRGVkZYL0ZlblEsMC4yNzc3Nzc4ZW1GJy9GaG5GZG8tSSNtbkdGJDYmUSIwRidGMkY1RjhGMkY1RkNGRUY4LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYvLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUklbXN1cEdGJDYlLUYsNiVRInhGJ0YvRjItSSNtbkdGJDYkUSIzRidGOS8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRictRjY2LVEiK0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EsMC4yMjIyMjIyZW1GJy9GTkZqbi1GVjYkUSwxLjMyMzg2NDA3NEYnRjktRjY2LVExJkludmlzaWJsZVRpbWVzO0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EmMC4wZW1GJy9GTkZjby1GUDYlRlItRlY2JFEiMkYnRjlGWS1GNjYtUSgmbWludXM7RidGOUY7Rj5GQEZCRkRGRkZIRmluRltvLUZWNiRRLDIuOTc0Mjc4OTY4RidGOS1GNjYtUSJ+RidGOUY7Rj5GQEZCRkRGRkZIRmJvRmRvRlJGam8tRlY2JFEtMC4yMjcxNzQ1MTg5RidGOQ==print(); # input 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print(); # input 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print(); # input 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print(); # input placeholderJSFHJSFHJSFH
<Text-field style="Heading 2" layout="Heading 2">Options</Text-field>output
output=value : returns the final numerical approximation of the root.output=animation : returns an animation showing the iterations of the root approximation process.output=plot : returns a plot of f with each iterative approximation shown and the relevant information about the numerical approximation displayed in the title of the plot.output=information : returns detailed information about the iterative approximations of the root of f.output=sequence : returns an expression sequence LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEicEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYkLUYvNiVRImtGJ0YyRjUvRjZRJ25vcm1hbEYnLyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGPQ==, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEia0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1JI21uR0YkNiRRIjBGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYtUSMuLkYnRjUvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj4vJSlzdHJldGNoeUdGPi8lKnN5bW1ldHJpY0dGPi8lKGxhcmdlb3BHRj4vJS5tb3ZhYmxlbGltaXRzR0Y+LyUnYWNjZW50R0Y+LyUnbHNwYWNlR1EsMC4yMjIyMjIyZW1GJy8lJ3JzcGFjZUdRJjAuMGVtRictRiw2JVEibkYnLyUnaXRhbGljR1EldHJ1ZUYnL0Y2USdpdGFsaWNGJ0Y1RitGNQ== that converges to the exact root for a sufficiently well-behaved function and initial approximation.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print(); # input 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%;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%;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print(); # input 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print(); # input placeholderJSFH
tolerance = positiveThe error tolerance of the approximation. The default value is LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkmbWZyYWNHRiQ2KC1JI21uR0YkNiRRIjFGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRi82JFEmMTAwMDBGJ0YyLyUubGluZXRoaWNrbmVzc0dGMS8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0Y8LyUpYmV2ZWxsZWRHUSZmYWxzZUYnRjI=. 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(); # input 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print(); # input 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print(); # input placeholderstoppingcriterion = relative, absolute, or function_valueThe criterion that the approximations must meet before discontinuing the iterations. The following describes each criterion:relative : 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 < toleranceabsolute : 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 < tolerancefunction_value : LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkobWZlbmNlZEdGJDYoLUYjNiYtSSNtaUdGJDYlUSJmRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2PlEwJkFwcGx5RnVuY3Rpb247RicvJSdmYW1pbHlHUTBUaW1lc35OZXd+Um9tYW5GJy8lJXNpemVHUSMxMkYnLyUlYm9sZEdRJmZhbHNlRicvRjVGRi8lKnVuZGVybGluZUdGRi8lKnN1YnNjcmlwdEdGRi8lLHN1cGVyc2NyaXB0R0ZGLyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GJy8lK2JhY2tncm91bmRHUS5bMjU1LDI1NSwyNTVdRicvJSdvcGFxdWVHRkYvJStleGVjdXRhYmxlR0ZGLyUpcmVhZG9ubHlHRkYvJSljb21wb3NlZEdGRi8lKmNvbnZlcnRlZEdGRi8lK2ltc2VsZWN0ZWRHRkYvJSxwbGFjZWhvbGRlckdGRi8lNnNlbGVjdGlvbi1wbGFjZWhvbGRlckdGRi9GOFEnbm9ybWFsRicvJSZmZW5jZUdGRi8lKnNlcGFyYXRvckdGRi8lKXN0cmV0Y2h5R0ZGLyUqc3ltbWV0cmljR0ZGLyUobGFyZ2VvcEdGRi8lLm1vdmFibGVsaW1pdHNHRkYvJSdhY2NlbnRHRkYvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZgcC1GLDYkLUYjNiQtSSVtc3ViR0YkNiUtRjE2JVEicEYnRjRGNy1GIzYkLUYxNiVRIm5GJ0Y0RjdGXm8vJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Zeb0Zeb0Zeb0Zeby9JK21zZW1hbnRpY3NHRiRRJGFic0YnLyUlb3BlbkdRKSZ2ZXJiYXI7RicvJSZjbG9zZUdGanFGZXFGXm8= < toleranceBy default, stoppingcriterion = relative.All other options below are detailed in the plot chapter.
<Text-field style="Heading 3" layout="Heading 3">more options</Text-field>functionoptions = listA list of options for the plot of the expression f. By default, f is plotted as a solid red line.lineoptions = listA list of options for the lines on the plot. By default the lines are solid blue.maxiterations = posintThe maximum number of iterations to to perform. The default value of maxiterations depends on which type of output is chosen:output = value: default maxiterations = 100output = sequence: default maxiterations = 10output = information: default maxiterations = 10output = plot: default maxiterations = 5output = animation: default maxiterations = 10plotoptions = listThe final plot options when output = plot or output = animation.pointoptions = listA list of options for the points on the plot. By default, the points are plotted as green circles.showfunction = truefalseWhether to display f on the plot or not. By default, this option is set to true.showlines = truefalseWhether to display lines that accentuate each approximate iteration when output = plot. By default, this option is set to true. To control the vertical lines, see the showverticallines and verticallineoptions options.showpoints = truefalseWhether to display the points at each approximate iteration on the plot when output = plot. By default, this option is set to true.showverticallines = truefalseWhether to display the vertical lines at each iterative approximation on the plot when output = plot.tickmarks = listThe tickmarks when output = plot or output = animation. By default, tickmarks are placed at the initial and final approximations with the labels LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEicEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYkLUkjbW5HRiQ2JFEiMEYnL0Y2USdub3JtYWxGJ0Y+LyUvc3Vic2NyaXB0c2hpZnRHRj1GPg== (or a and b for two initial approximates) and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEicEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYkLUYvNiVRIm5GJ0YyRjUvRjZRJ25vcm1hbEYnLyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGPQ==, where LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= is the total number of iterations used to reach the final approximation. See plot/tickmarks for more detail on specifying tickmarks.title = stringA title for the plot. The default title contains general information concerning the approximation. For more information about specifying a title, see plot/typesetting.verticallineoptions = listA list of options for the vertical lines on the plot. By default, the lines are dashed and blue.view = [realcons..realcons, realcons..realcons]The plot view of the plot when output = plot. See plot/options for more information.JSFHJSFHLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=JSFH
<Text-field style="Heading 1" layout="Heading 1">Finite Differences</Text-field>Maple does not have prepared templates of the Finite Differences Operators, But using Maple you can create those operators (in very easy way which will be shown below) and in order to use them you need only to call the operator and eval the wanted value to the operator. print(); # input placeholder
<Text-field style="Heading 2" layout="Heading 2">Operators</Text-field>LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
<Text-field style="Heading 3" layout="Heading 3">shift</Text-field>LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIjpGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JJ21zcGFjZUdGJDYmLyUnaGVpZ2h0R1EmMC4wZXhGJy8lJndpZHRoR1EmMC4wZW1GJy8lJmRlcHRoR0ZULyUqbGluZWJyZWFrR1EobmV3bGluZUYnLUZQNiZGUkZVRlgvRmVuUSVhdXRvRictRiw2JVEqaW50ZXJmYWNlRidGL0YyLUkobWZlbmNlZEdGJDYkLUYjNiUtRiw2JVEsdHlwZXNldHRpbmdGJ0YvRjItRjY2LVEiPUYnRjlGO0Y+RkBGQkZERkZGSEZKRk0tRiw2JVEpZXh0ZW5kZWRGJ0YvRjJGOUY1LUYsNiNRIUYnJSFHJSFHLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYwLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUYsNiVRInhGJ0YvRjItRjY2LVEoJnNyYXJyO0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EmMC4wZW1GJy9GTkZWLUYsNiVRImFGJ0YvRjItRjY2LVEnJnNkb3Q7RidGOUY7Rj5GQEZCRkRGRkZIRlVGVy1JJW1zdXBHRiQ2JUZPLUYjNiMtSSNtbkdGJDYkUSIyRidGOS8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRictRjY2LVEiK0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EsMC4yMjIyMjIyZW1GJy9GTkZoby1GLDYlUSJiRidGL0YyRmVuRk9GZG8tRiw2JVEiY0YnRi9GMi1GNjYtUSI6RidGOUY7Rj5GQEZCRkRGRkZIRkpGTQ==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiRUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUYsNiVRJXN1YnNGJ0YvRjItSShtZmVuY2VkR0YkNiQtRiM2LC1GLDYlUSJ4RidGL0YyLUY2Ni1RIj1GJ0Y5RjtGPkZARkJGREZGRkhGSkZNRlctRjY2LVEiK0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EsMC4yMjIyMjIyZW1GJy9GTkZbby1GLDYlUSJwRidGL0YyLUY2Ni1RJyZzZG90O0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EmMC4wZW1GJy9GTkZkby1GLDYlUSJoRidGL0YyLUY2Ni1RIixGJ0Y5RjsvRj9GMUZARkJGREZGRkhGY28vRk5RLDAuMzMzMzMzM2VtRictRiw2JVEiZkYnRi9GMi1GUzYkLUYjNiNGV0Y5Rjk=print(); # input placeholderJSFHJSFH
<Text-field style="Heading 3" layout="Heading 3">Backward differences</Text-field>LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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print(); # input placeholderJSFHJSFH
<Text-field style="Heading 3" layout="Heading 3">forward differences</Text-field>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(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYwLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUYsNiVRInhGJ0YvRjItRjY2LVEoJnNyYXJyO0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EmMC4wZW1GJy9GTkZWLUYsNiVRImFGJ0YvRjItRjY2LVEnJnNkb3Q7RidGOUY7Rj5GQEZCRkRGRkZIRlVGVy1JJW1zdXBHRiQ2JUZPLUYjNiMtSSNtbkdGJDYkUSIyRidGOS8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRictRjY2LVEiK0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EsMC4yMjIyMjIyZW1GJy9GTkZoby1GLDYlUSJiRidGL0YyRmVuRk9GZG8tRiw2JVEiY0YnRi9GMi1GNjYtUSI6RidGOUY7Rj5GQEZCRkRGRkZIRkpGTQ==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYjLUYvNiVRKGZvcndhcmRGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnL0Y2USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGSC8lKXN0cmV0Y2h5R0ZILyUqc3ltbWV0cmljR0ZILyUobGFyZ2VvcEdGSC8lLm1vdmFibGVsaW1pdHNHRkgvJSdhY2NlbnRHRkgvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZXLUYvNiVRJXN1YnNGJ0YyRjUtSShtZmVuY2VkR0YkNiQtRiM2Ky1GLzYlUSJ4RidGMkY1LUZBNi1RIj1GJ0ZERkZGSUZLRk1GT0ZRRlNGVUZYRlxvLUZBNi1RIitGJ0ZERkZGSUZLRk1GT0ZRRlMvRlZRLDAuMjIyMjIyMmVtRicvRllGZm8tRi82JVEiaEYnRjJGNS1GQTYtUSJ+RidGREZGRklGS0ZNRk9GUUZTL0ZWUSYwLjBlbUYnL0ZZRl9wLUZBNi1RIixGJ0ZERkYvRkpGNEZLRk1GT0ZRRlNGXnAvRllRLDAuMzMzMzMzM2VtRidGLi1GaG42JC1GIzYjRlxvRkRGRC1GQTYtUSgmbWludXM7RidGREZGRklGS0ZNRk9GUUZTRmVvRmdvRi5GZ3A=print(); # input placeholderJSFH
<Text-field style="Heading 3" layout="Heading 3">centeral differences</Text-field>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(); # input placeholderJSFHJSFH
<Text-field style="Heading 3" layout="Heading 3">average differences</Text-field>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print(); # input placeholderJSFHJSFH
<Text-field style="Heading 3" layout="Heading 3">Derivative</Text-field>LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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print(); # input placeholderJSFHLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
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<Text-field style="Heading 2" layout="Heading 2">Interpolation</Text-field>Perform polynomial interpolation on a set of dataLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=PolynomialInterpolation(xy, opts)LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
xy-list(numeric), list(list(numeric, numeric)), list(list(numeric, numeric, numeric)); the data points to be interpolatedopts-equation(s) of the form keyword=value where keyword is one of digits, errorboundvar, extrapolate, function, independentvar, method; the options for interpolating the data xy
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print(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEpd2hhdHR5cGVGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2Iy1GLDYlUSN4eUYnRi9GMi9GM1Enbm9ybWFsRic=print(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRictRiM2JS1GLDYlUSV3aXRoRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2PlEwJkFwcGx5RnVuY3Rpb247RicvJSdmYW1pbHlHUTBUaW1lc35OZXd+Um9tYW5GJy8lJXNpemVHUSMxMkYnLyUlYm9sZEdRJmZhbHNlRicvRjVGRi8lKnVuZGVybGluZUdGRi8lKnN1YnNjcmlwdEdGRi8lLHN1cGVyc2NyaXB0R0ZGLyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GJy8lK2JhY2tncm91bmRHUS5bMjU1LDI1NSwyNTVdRicvJSdvcGFxdWVHRkYvJStleGVjdXRhYmxlR0ZGLyUpcmVhZG9ubHlHRkYvJSljb21wb3NlZEdGRi8lKmNvbnZlcnRlZEdGRi8lK2ltc2VsZWN0ZWRHRkYvJSxwbGFjZWhvbGRlckdGRi8lNnNlbGVjdGlvbi1wbGFjZWhvbGRlckdGRi9GOFEnbm9ybWFsRicvJSZmZW5jZUdGRi8lKnNlcGFyYXRvckdGRi8lKXN0cmV0Y2h5R0ZGLyUqc3ltbWV0cmljR0ZGLyUobGFyZ2VvcEdGRi8lLm1vdmFibGVsaW1pdHNHRkYvJSdhY2NlbnRHRkYvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZgcC1JKG1mZW5jZWRHRiQ2JC1GIzYlRistRiM2JC1GLDYlUShTdHVkZW50RidGNEY3LUZkcDYmLUYjNiVGKy1GIzYjLUYsNiVRMk51bWVyaWNhbEFuYWx5c2lzRidGNEY3RitGXm8vJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRidGK0Zeby1GOzYtUSI6RidGXm9GYG9GYm9GZG9GZm9GaG9Gam9GXHAvRl9wUSwwLjI3Nzc3NzhlbUYnL0ZicEZgcg==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiTEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIzo9RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtRiM2JS1GLDYlUThQb2x5bm9taWFsSW50ZXJwb2xhdGlvbkYnRi9GMi1GNjY+UTAmQXBwbHlGdW5jdGlvbjtGJy8lJ2ZhbWlseUdRMFRpbWVzfk5ld35Sb21hbkYnLyUlc2l6ZUdRIzEyRicvJSVib2xkR0Y9L0YwRj0vJSp1bmRlcmxpbmVHRj0vJSpzdWJzY3JpcHRHRj0vJSxzdXBlcnNjcmlwdEdGPS8lK2ZvcmVncm91bmRHUShbMCwwLDBdRicvJStiYWNrZ3JvdW5kR1EuWzI1NSwyNTUsMjU1XUYnLyUnb3BhcXVlR0Y9LyUrZXhlY3V0YWJsZUdGPS8lKXJlYWRvbmx5R0Y9LyUpY29tcG9zZWRHRj0vJSpjb252ZXJ0ZWRHRj0vJStpbXNlbGVjdGVkR0Y9LyUscGxhY2Vob2xkZXJHRj0vJTZzZWxlY3Rpb24tcGxhY2Vob2xkZXJHRj1GOUY7Rj5GQEZCRkRGRkZIL0ZLUSYwLjBlbUYnL0ZORmdwLUkobWZlbmNlZEdGJDYkLUYjNiMtRiw2JVEjeHlGJ0YvRjJGOS1GLDYjUSFGJw==print(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnZXhwYW5kRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiQtRiw2JVEsSW50ZXJwb2xhbnRGJ0YvRjItRjY2JC1GIzYjLUYsNiVRIkxGJ0YvRjIvRjNRJ25vcm1hbEYnRkQ=print(); # input 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print(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRictRiM2JC1GLDYlUSdleHBhbmRGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYlUSxJbnRlcnBvbGFudEYnRjRGNy1GOzYkLUYjNiMtRiw2JVEiTEYnRjRGNy9GOFEnbm9ybWFsRidGSUYrprint(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=JSFHJSFH
<Text-field style="Heading 1" layout="Heading 1">ODE numerical solution</Text-field>In this chapter we present several numerical solution for ODE: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Any of the following methods can be used:EulerTaylorRunge-Kutta MidpointRunge-Kutta Order ThreeRunge-Kutta Order FourRunge-Kutta-FehlbergRunge-Kutta HeunRunge-Kutta Modified EulerAdams-Bashforth Two-StepAdams-Bashforth Three-StepAdams-Bashforth Four-StepAdams-Bashforth Five-StepAdams-Moulton Two-StepAdams-Moulton Three-StepAdams-Moulton Four-StepAdams-Bashforth-Moulton Second-Order Predictor-CorrectorAdams-Bashforth-Moulton Third-Order Predictor-CorrectorAdams-Bashforth-Moulton Fourth-Order Predictor-CorrectorAdams-Bashforth-Moulton Fifth-Order Predictor-Corrector
<Text-field style="Heading 2" layout="Heading 2">Euler method</Text-field>Numerically approximate the solution to a first order initial-value problem using Euler's method.JSFHJSFHEuler(ODE, IC, t=b, opts)Euler(ODE, IC, b, opts)
ODE-equation; first order ordinary differential equation of the form 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-equation; initial condition of the form y(a)=c, where a is the left endpoint of the initial-value problemt-name; the independent variableb-algebraic; the point for which to solve; the right endpoint of this initial-value problemopts-(optional) equations of the form keyword=value, where keyword is one of numsteps, output, comparewith, digits, or plotoptions; options for numerically solving the initial-value problem
LUkmRXVsZXJHNiI2JS8tSSVkaWZmRyUqcHJvdGVjdGVkRzYkLUkieUdGJDYjSSJ0R0YkRi4tSSRjb3NHRiRGLS8tRiw2IyIiISQiIiYhIiIvRi4iIiQ=print(); # input placeholderPloting Euler method - changing the value of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= will change the red plot.LUkmRXVsZXJHNiI2Ji8tSSVkaWZmRyUqcHJvdGVjdGVkRzYkLUkieUdGJDYjSSJ0R0YkRi4tSSRjb3NHNiRGKUkoX3N5c2xpYkdGJEYtLy1GLDYjIiIhJCIiJiEiIi9GLiIiJC9JJ291dHB1dEdGJEklcGxvdEdGMQ==%;JSFHJSFH
<Text-field style="Heading 2" layout="Heading 2">Taylor method</Text-field>Given an initial-value problem consisting of an ordinary differential equation ODE, a range LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RJiZsZXE7RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtRiw2JVEidEYnRi9GMkY1LUYsNiVRImJGJ0YvRjJGOQ==, and an initial condition y(a) = c, the Taylor command computes an approximate value of y(b) by expanding y(t) into a Taylor polynomial at each step along the interval.Taylor(ODE, IC, t=b, opts)Taylor(ODE, IC, b, opts)
ODE-equation; first order ordinary differential equation of the form 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-equation; initial condition of the form y(a)=c, where a is the left endpoint of the initial-value problemt-name; the independent variableb-algebraic; the point for which to solve; the right endpoint of this initial-value problemopts-(optional) equations of the form keyword=value, where keyword is one of numsteps, output, comparewith, digits, order, or plotoptions; options for numerically solving the initial-value problem
LUknVGF5bG9yRzYiNiUvLUklZGlmZkclKnByb3RlY3RlZEc2JC1JInlHRiQ2I0kidEdGJEYuLUkkY29zRzYkRilJKF9zeXNsaWJHRiRGLS8tRiw2IyIiISQiIiYhIiIvRi4iIiQ=print(); # input placeholderPloting Taylor method - changing the value of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= will change the red plot.LUknVGF5bG9yRzYiNiYvLUklZGlmZkclKnByb3RlY3RlZEc2JC1JInlHRiQ2I0kidEdGJEYuLUkkY29zRzYkRilJKF9zeXNsaWJHRiRGLS8tRiw2IyIiISQiIiYhIiIvRi4iIiQvSSdvdXRwdXRHRiRJJXBsb3RHRjE=%;JSFHJSFH
<Text-field style="Heading 2" layout="Heading 2">RungeKutta</Text-field>Given an initial-value problem consisting of an ordinary differential equation ODE, a range LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RJiZsZXE7RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtRiw2JVEidEYnRi9GMkY1LUYsNiVRImJGJ0YvRjJGOQ== , and an initial condition y(a) = c, the RungeKutta command computes an approximate value of y(b) using the Runge-Kutta methods.RungeKutta(ODE, IC, t=b, opts)RungeKutta(ODE, IC, b, opts)
ODE-equation; first order ordinary differential equation of the form 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-equation; initial condition of the form y(a)=c, where a is the left endpoint of the initial-value problemt-name; the independent variableb-algebraic; the point for which to solve; the right endpoint of this initial-value problemopts-(optional) equations of the form keyword=value, where keyword is one of numsteps, output, comparewith, digits, plotoptions, or submethod; options for numerically solving the initial-value problem
LUkrUnVuZ2VLdXR0YUc2IjYlLy1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJ5R0YkNiNJInRHRiRGLi1JJGNvc0c2JEYpSShfc3lzbGliR0YkRi0vLUYsNiMiIiEkIiImISIiL0YuIiIkprint(); # input placeholderPloting RungeKutta method - changing the value of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= will change the red plot.LUkrUnVuZ2VLdXR0YUc2IjYmLy1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJ5R0YkNiNJInRHRiRGLi1JJGNvc0c2JEYpSShfc3lzbGliR0YkRi0vLUYsNiMiIiEkIiImISIiL0YuIiIkL0knb3V0cHV0R0YkSSVwbG90R0Yx%;LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=JSFH
<Text-field style="Heading 2" layout="Heading 2">Multisteps method - AdamsBashforth method</Text-field>Given an initial-value problem consisting of an ordinary differential equation ODE, a range LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RJiZsZXE7RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtRiw2JVEidEYnRi9GMkY1LUYsNiVRImJGJ0YvRjJGOQ== , and an initial condition y(a) = c, the AdamsBashforth command computes an approximate value of y(b) using one of the Adams-Bashforth Methods (a family of explicit multi-step methods).AdamsBashforth(ODE, IC, t=a..b, opts)AdamsBashforth(ODE, IC, a..b, opts)
ODE-equation; first order ordinary differential equation of the form 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-equation; initial condition of the form y(a)=c, where a is the left endpoint of the initial-value problemt-name; the independent variableb-algebraic; the point for which to solve; the right endpoint of this initial-value problemopts-(optional) equations of the form keyword=value, where keyword is one of numsteps, output, comparewith, digits, plotoptions, or submethod; options for numerically solving the initial-value problem
submethod = step2, step3, step4, or step5The order of the difference formula used to solve this initial-value problem.step2 = Two-Step Method (with a local truncation error proportional to LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2JC1JJW1zdXBHRiQ2JS1GLDYlUSJoRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW5HRiQ2JFEiM0YnL0Y7USdub3JtYWxGJy8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRidGQUYrRkE=, where LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiaEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= is the step size)step3 = Three-Step Method (with a local truncation error proportional to LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2JC1JJW1zdXBHRiQ2JS1GLDYlUSJoRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW5HRiQ2JFEiNEYnL0Y7USdub3JtYWxGJy8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRidGQUYrRkE=)step4 = Four-Step Method (with a local truncation error proportional to LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2JC1JJW1zdXBHRiQ2JS1GLDYlUSJoRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW5HRiQ2JFEiNUYnL0Y7USdub3JtYWxGJy8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRidGQUYrRkE=)step5 = Five-Step Method (with a local truncation error proportional to LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2JC1JJW1zdXBHRiQ2JS1GLDYlUSJoRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW5HRiQ2JFEiNkYnL0Y7USdub3JtYWxGJy8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRidGQUYrRkE=)By default the Four-Step submethod is used.LUkvQWRhbXNCYXNoZm9ydGhHNiI2Ji8tSSVkaWZmRyUqcHJvdGVjdGVkRzYkLUkieUdGJDYjSSJ0R0YkRi4tSSRjb3NHNiRGKUkoX3N5c2xpYkdGJEYtLy1GLDYjIiIhJCIiJiEiIi9GLiIiJC9JKnN1Ym1ldGhvZEdGJEkmc3RlcDJHRiQ=print(); # input placeholderPloting AdamsBashforth method - changing the value of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= will change the red plot.LUkvQWRhbXNCYXNoZm9ydGhHNiI2Jy8tSSVkaWZmRyUqcHJvdGVjdGVkRzYkLUkieUdGJDYjSSJ0R0YkRi4tSSRjb3NHNiRGKUkoX3N5c2xpYkdGJEYtLy1GLDYjIiIhJCIiJiEiIi9GLiIiJC9JKnN1Ym1ldGhvZEdGJEkmc3RlcDJHRiQvSSdvdXRwdXRHRiRJJXBsb3RHRjE=%;JSFH
<Text-field style="Heading 2" layout="Heading 2">Predictor-Correction method (Adams-Bashforth-Moulton) </Text-field>Numerically approximate the solution to a first order initial-value problem with the fourth-order Adams-Bashforth-Moulton Method.Given an initial-value problem consisting of an ordinary differential equation ODE, a range 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, and an initial condition y(LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=) = c, the AdamsBashforthMoulton command computes an approximate value of y(LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiYkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=) using one of the Adams-Bashforth-Moulton family of predictor-corrector methods.AdamsBashforthMoulton(ODE, IC, t=b, opts)AdamsBashforthMoulton(ODE, IC, b, opts)
ODE-equation; first order ordinary differential equation of the form 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-equation; initial condition of the form y(a)=c, where a is the left endpoint of the initial-value problemt-name; the independent variableb-algebraic; the point for which to solve; the right endpoint of this initial-value problemopts-(optional) equations of the form keyword=value, where keyword is one of numsteps, output, comparewith, digits, plotoptions, or submethod; options for numerically solving the initial-value problem
LUk2QWRhbXNCYXNoZm9ydGhNb3VsdG9uRzYiNiUvLUklZGlmZkclKnByb3RlY3RlZEc2JC1JInlHRiQ2I0kidEdGJEYuLUkkY29zRzYkRilJKF9zeXNsaWJHRiRGLS8tRiw2IyIiISQiIiYhIiIvRi4iIiQ=print(); # input placeholderPloting AdamsBashforth method: changing t value will change the red plot.LUk2QWRhbXNCYXNoZm9ydGhNb3VsdG9uRzYiNiYvLUklZGlmZkclKnByb3RlY3RlZEc2JC1JInlHRiQ2I0kidEdGJEYuLUkkY29zRzYkRilJKF9zeXNsaWJHRiRGLS8tRiw2IyIiISQiIiYhIiIvRi4iIiQvSSdvdXRwdXRHRiRJJXBsb3RHRjE=%;JSFHJSFH
<Text-field style="Heading 2" opaque="true" background="[255,255,0]" layout="Heading 2"><Font opaque="false" background="[255,255,255]">ODE system numerical solution</Font></Text-field>First, we need to write the equations in 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 format.After having the system in the propriate format we can enter the vector/ matrix to the methods above.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=JSFH
<Text-field style="Heading 1" layout="Heading 1">Linear Algebra Systems</Text-field>In this chapter we deal with finding the numerical solutions for N equations with N variables.We will presnet the problem in the next format 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As we know, the system above has solution as long as det(A)LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbW9HRiQ2LVErJk5vdEVxdWFsO0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZDRi8=0.
<Text-field style="Heading 2" layout="Heading 2">Direct methods to solve <Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation></Text-field>
<Text-field style="Heading 3" layout="Heading 3">Gauss</Text-field>Look at LinearAlgebra chapter, or in the following linkGaussianEliminationprint(); # input placeholderJSFH
<Text-field style="Heading 3" layout="Heading 3">GaussJordan</Text-field>Look at LinearAlgebra chapter, or in the following linkGaussJordanJSFH
<Text-field style="Heading 3" layout="Heading 3">LU decomposition</Text-field>Look at LinearAlgebra chapter, or in the following linkLU decompositionJSFH
<Text-field style="Heading 2" layout="Heading 2">Iterative methods to solve <Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation></Text-field>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print(); # input placeholderCompute an iterative formula to approximate the solution to a linear system numerically.Given a system 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, the IterativeFormula command computes an equivalent fixed-point system of the form 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.The IterativeFormula command can compute the iteration matrix LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiVEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2ZvcmVncm91bmRHUShbMCwwLDBdRicvJTBmb250X3N0eWxlX25hbWVHUSgyRH5NYXRoRicvRjNRJ25vcm1hbEYn and vector LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiY0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2ZvcmVncm91bmRHUShbMCwwLDBdRicvJTBmb250X3N0eWxlX25hbWVHUSgyRH5NYXRoRicvRjNRJ25vcm1hbEYn for the following methods: the Gauss-Seidel iterative, Jacobi iterative, and successive over-relaxation method.IterativeFormula(A, b, opts)IterativeFormula(A, opts)
A-Matrix; a square (LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=-by-LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=) matrix or an augmented LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=-by-LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJuRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiK0YnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JFEiMUYnRj5GPkYrRj4= matrix of the form (A|b)b-(optional) Vector; a vector of length LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=opts-(optional) equation(s) of the form keyword=value where keyword is one of digits, initialapprox, iterations, method, output, showsteps; the options for computing the iterative formula
To show the difference betwin the methods we will take a matrix A and vector B:PkkiQUc2Ii1JJ01hdHJpeEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjNyY3JiQiIzUhIiIkRi9GLyQiIiMiIiEkRjNGMzcmRjAkIiM2Ri9GMCQiIiRGMzcmJEYyRi9GMEYtRjA3JkY0JEY5Ri9GMCQiIilGLw==print(); # input placeholderPkkiQkc2Ii1JJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjNyYkIiInISIiJCIjREYuJCEjNkYuJCIjOkYuprint(); # input placeholder
<Text-field style="Heading 3" layout="Heading 3">Jacobi method</Text-field>JSFHLUkxSXRlcmF0aXZlRm9ybXVsYUc2IjYnSSJBR0YkSSJCR0YkL0knbWV0aG9kR0YkSSdqYWNvYmlHRiQvSSdkaWdpdHNHRiQiIiQvSSdvdXRwdXRHRiQ3JC5JIlRHRiQuSSJjR0Ykprint(); # input placeholderLUktSXNDb252ZXJnZW50RzYiNiRJIkFHRiQvSSdtZXRob2RHRiRJJ2phY29iaUdGJA==print(); # input placeholderJSFHJSFH
<Text-field style="Heading 3" layout="Heading 3">Gauss-Seidel method</Text-field>LUkxSXRlcmF0aXZlRm9ybXVsYUc2IjYnSSJBR0YkSSJCR0YkL0knbWV0aG9kR0YkSSxnYXVzc3NlaWRlbEdGJC9JJ2RpZ2l0c0dGJCIiJC9JJ291dHB1dEdGJDckLkkiVEdGJC5JImNHRiQ=print(); # input placeholderLUktSXNDb252ZXJnZW50RzYiNiRJIkFHRiQvSSdtZXRob2RHRiRJLGdhdXNzc2VpZGVsR0Ykprint(); # input placeholderJSFHJSFHJSFH
<Text-field style="Heading 3" size="16" layout="Heading 3"><Font size="16">SOR - successive over-relaxation method</Font></Text-field>JSFHLUkxSXRlcmF0aXZlRm9ybXVsYUc2IjYnSSJBR0YkSSJCR0YkL0knbWV0aG9kR0YkLUkkU09SR0YkNiMiIiIvSSdkaWdpdHNHRiQiIiQvSSdvdXRwdXRHRiQ3JC5JIlRHRiQuSSJjR0Ykprint(); # input placeholderLUktSXNDb252ZXJnZW50RzYiNiRJIkFHRiQvSSdtZXRob2RHRiQtSSRTT1JHRiQ2IyIiIg==print(); # input placeholderJSFHJSFHLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=JSFHLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=JSFHTTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDc0MzQzMTc2NTQyWCwlJ3NmbG9hdEc2IkYlW2dsISIlISEhIzEiJSIlJCIiIUYnJCIkNCohIiUkISQrIyEiJEYmJCIkKyJGLUYmRi4kISR2JEYtJEYsISIjRihGJiQiJEQiRi1GJiQhJHQjRjNGLkYmRiU=TTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDc0MzQzMTgzNzc0WCwlJ3NmbG9hdEc2IkYlW2dsISIlISEhIzEiJSIlJCIiIUYnRiZGJkYmJCIkKyIhIiQkIiQ0KiEiJiQhJCI+ISIlJCEkIWVGLSQhJCsjISIjJCEkNipGMCQiJCJSRiokIiRJKUYwRiYkISR0I0Y1JCEkdCJGKiRGKUY1RiU=TTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDc0MzQzMTg0MTM0WColJ3NmbG9hdEc2IkYlW2dsISMlISEhIiUiJSQiJCsnISIkJCIkSyMhIiMkISQpKSpGKCQiJCMpKUYoRiU=TTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDc0MzQzMjA5MzEwWCwlJ3NmbG9hdEc2IkYlW2dsISIlISEhIzEiJSIlJCIiIUYnRiZGJkYmJCIkKyIhIiQkIiQ0KiEiJiQhJCI+ISIlJCEkIWVGLSQhJCsjISIjJCEkNipGMCQiJCJSRiokIiRJKUYwRiYkISR0I0Y1JCEkdCJGKiRGKUY1RiU=TTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDc0MzQzMjA5NzkwWColJ3NmbG9hdEc2IkYlW2dsISMlISEhIiUiJSQiJCsnISIkJCIkSyMhIiMkISQpKSpGKCQiJCMpKUYoRiU=