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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