Description:

This notebook illustrates DifferentialEquations`LdeApprox` package capability of doing polynomial approximation of a solution of an LDE with regular singular points. First of all we load LdeApprox package and define a BVP with regular singular point. Then we use ApproxSol procedure to find 3-rd degree polynomial approximation for the BVP 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.

Boundary value problem.

Finding polynomial approximation for solution of the BVP.

Unfortunately DSolve can not find exact solution of the BVP.

Nevertheless the exact solution is as follows.

Comparing exact and approximate results using Mathematica™ function Plot3D.