BVP examples of the AnalyticalApproximations`LdeApprox` package
Copyright © 2003-2017 DigiArea, Inc.. All rights reserved.
This notebook illustrates AnalyticalApproximations`LdeApprox` package capability of working with BVPs.
This loads the package.
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Example 1
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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Comparing exact and approximate results for 
using Mathematica function Plot.
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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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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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Comparing exact and approximate results using Mathematica function Plot3D.
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Example 4
Boundary value problem.
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Trying to find polynomial approximation for solution of the BVP.
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Using ToRatCoeffs function to get rational coefficients of the LDE on interval [0,1].
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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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Comparing exact and approximate results using Mathematica function Plot.
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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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Using Mathematica function DSolve to get exact solution of the BVP.
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Comparing exact and approximate results using Mathematica function Plot.
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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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Using Mathematica function DSolve to get exact solution of the BVP.
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Comparing exact and approximate results using Mathematica function Plot.
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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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Using Mathematica function DSolve to get exact solution of the BVP.
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Comparing exact and approximate results using Mathematica function Plot3D.
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Example 8
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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Comparing exact and approximate results.
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Example 9
Polynomial approximation of solution of boundary value problem 
.
The boundary value problem.
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Finding polynomial approximation for solution of the BVP.
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Finding normalized polynomial approximation for solution of the BVP on interval [0,1].
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Unfortunately DSolve can not find exact solution of the BVP because it contains parameter α.
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As the BVP is homogeneous one then to get the exact solution we can use the following technic. First of all we find exact solution for the following problem 
. After that we find constant α. And finally we normalize the result to get exact solution of the initial BVP.
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Finding constant α using the exact solution.
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Comparing exact and approximate results for constant α.
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Finding normalized exact solution of the BVP on interval [0,1].
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Comparing normalized exact and approximate results using Mathematica function Plot.
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