• RSP example of the AnalyticalApproximations`LdeApprox` package

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    This notebook illustrates AnalyticalApproximations`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.

  • [Graphics:Mathematica/LdeApprox/rsp/images/index_gr_1.gif]


  • Boundary value problem.

  • [Graphics:Mathematica/LdeApprox/rsp/images/index_gr_2.gif]
  • Finding polynomial approximation for solution of the BVP.

  • [Graphics:Mathematica/LdeApprox/rsp/images/index_gr_4.gif]
  • Unfortunately DSolve can not find exact solution of the BVP.

  • [Graphics:Mathematica/LdeApprox/rsp/images/index_gr_7.gif]
  • Nevertheless the exact solution is as follows.

  • [Graphics:Mathematica/LdeApprox/rsp/images/index_gr_9.gif]
  • Comparing exact and approximate results using Mathematica™ function Plot3D.

  • [Graphics:Mathematica/LdeApprox/rsp/images/index_gr_11.gif]



    The method applied in the package is a numerically - analytical one. It means that you can use symbolic expressions as boundary conditions, interval of approximation etc. However these kind of examples leads to huge output so its not for Web. This reason force us to introduce simple example with no parameters. You can try more complex examples in your computer.