Numerical example of the AnalyticalApproximations`LdeApprox` package Copyright © 2004-2016 DigiArea, Inc. All rights reserved. Description:
This notebook illustrates AnalyticalApproximations`LdeApprox` package capability of doing numerical polynomial approximation of an LDE solution.First of all we load the package and define an IVP. Then we use ApproxSol procedure to find 5-th degree polynomial approximation for the IVP solution on interval x = [0,1]. After that we find exact solution by Mathematica™ function DSolve. Finally we compare exact and approximate results using Mathematica™ function Plot. This loads the package.
Initial value problem.
Finding polynomial approximation for solution of the IVP.
UnfortunatelyDSolvecan not find exact solution of the IVP.
Nevertheless the exact solution is as follows.
Comparing exact and approximate results using Mathematica™ function Plot.
Note: The example is quite simple (just for Web). You can try more complex examples in your computer. |