RSP examples of the AnalyticalApproximations`LdeApprox` package

Copyright © 2003-20011DigiArea, Inc.. All rights reserved.

This notebook illustrates AnalyticalApproximations`LdeApprox` package capability of doing polynomial approximation of a solution of an LDE with regular singular points.

This loads the package.

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Example 1

Simple boundary value problem.

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Finding polynomial approximation for solution of the BVP.

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Using Mathematica function DSolve to get exact solution of the BVP.

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More compact result is as follows.

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Comparing exact and approximate results using Mathematica function Plot3D.

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Comparing exact and approximate results for n = 3.

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Example 2

Boundary value problem.

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Finding polynomial approximation for solution of the BVP.

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Using Mathematica function DSolve to get exact solution of the BVP.

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In fact the result is as follows.

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Comparing exact and approximate results using Mathematica function Plot3D.

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Example 3

Boundary value problem.

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Finding polynomial approximation for solution of the BVP.

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Using Mathematica function DSolve to get exact solution of the BVP.

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More compact result is as follows.

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Comparing exact and approximate results using Mathematica function Plot3D.

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Example 4

Boundary value problem.

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Finding polynomial approximation for solution of the BVP.

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Unfortunately DSolve can not find exact solution of the BVP.

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Nevertheless the exact solution is as follows.

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Comparing exact and approximate results using Mathematica function Plot3D.

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Example 5

Boundary value problem.

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Finding polynomial approximation for solution of the BVP.

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Exact solution of the BVP.

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More compact result.

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Comparing exact and approximate results using Mathematica function Plot3D.

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Example 6

Boundary value problem.

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Finding polynomial approximation for solution of the BVP.

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Unfortunately DSolve can not find exact solution of the BVP.

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Nevertheless the exact solution is as follows.

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Comparing exact and approximate results using Mathematica function Plot3D.

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Example 7

Boundary value problem.

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Finding polynomial approximation for solution of the BVP.

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Unfortunately DSolve can not find exact solution of the BVP.

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Nevertheless the exact solution is as follows.

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Comparing exact and approximate results using Mathematica function Plot3D.

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