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.