Modified a-method examples of the AnalyticalApproximations`LdeApprox` package
Copyright © 2003-2011DigiArea, Inc.. All rights reserved..
This notebook illustrates AnalyticalApproximations`LdeApprox` package capability of doing polynomial approximation of an LDE solution using modified a-method.
This loads the package.
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This loads Graphics`Legend package (just for best presentation of the results).
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Example 1
Initial value problem.
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Finding polynomial approximation for solution of the IVP.
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Finding polynomial approximation for solution of the IVP using modified method with k = 1.
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Finding polynomial approximation for solution of the IVP using modified method with k = 2.
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Using Mathematica function DSolve tot find exact solution of the IVP.
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Comparing exact and approximate results using Mathematica function Plot. In this case modified method (for k=2) gives more uniform and pricise appoximation.
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Example 2
Initial value problem.
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Finding polynomial approximation for solution of the IVP.
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Using Mathematica function DSolve tot find exact solution of the IVP.
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Comparing exact and approximate results using Mathematica function Plot. In this case modified method gives quite bad appoximation.
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Example 3
Initial value problem.
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Finding polynomial approximation for solution of the IVP.
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Modified method is not avilable if leading polynom (coefficient of higher derivative) has zeros on the interval of approximation.
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Using Mathematica function DSolve tot find exact solution of the IVP.
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