• Simple example of the AnalyticalApproximations`LdeApprox` package

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    All rights reserved.

    Description:

    This notebook illustrates AnalyticalApproximations`LdeApprox` package capability of doing polynomial approximation of solution of simple LDE. First of all we load LdeApprox package and define simple IVP. Then we use ApproxSol procedure to find 7-th degree polynomial approximation for the IVP solution on interval x = [-h, h]. After that we find exact solution by Mathematica™ function DSolve . Finally we compare exact and approximate results using Mathematica®™ function Plot3D.
     

  • This loads the package.

  • [Graphics:Mathematica/LdeApprox/simple/images/index_gr_1.gif]
  • This is a simple IVP with parameter ξ.

  • [Graphics:Mathematica/LdeApprox/simple/images/index_gr_2.gif]
    [Graphics:Mathematica/LdeApprox/simple/images/index_gr_3.gif]
  • Finding polynomial approximation of the IVP solution on interval [-h,h].

  • [Graphics:Mathematica/LdeApprox/simple/images/index_gr_4.gif]
    [Graphics:Mathematica/LdeApprox/simple/images/index_gr_5.gif]
  • Finding exact solution of the IVP using Mathematica™ function DSolve.

  • [Graphics:Mathematica/LdeApprox/simple/images/index_gr_6.gif]
    [Graphics:Mathematica/LdeApprox/simple/images/index_gr_7.gif]
  • Comparing exact and approximate results for [Graphics:Mathematica/LdeApprox/simple/images/index_gr_8.gif] and [Graphics:Mathematica/LdeApprox/simple/images/index_gr_9.gif]

  • [Graphics:Mathematica/LdeApprox/simple/images/index_gr_10.gif]

    [Graphics:Mathematica/LdeApprox/simple/images/index_gr_11.gif]

    [Graphics:Mathematica/LdeApprox/simple/images/index_gr_12.gif]
  • Comparing exact and approximate results for [Graphics:Mathematica/LdeApprox/simple/images/index_gr_13.gif] using Mathematica™ function Plot3D.

  • [Graphics:Mathematica/LdeApprox/simple/images/index_gr_14.gif]

    [Graphics:Mathematica/LdeApprox/simple/images/index_gr_15.gif]

    [Graphics:Mathematica/LdeApprox/simple/images/index_gr_16.gif]
  • Comparing exact and approximate results in point [Graphics:Mathematica/LdeApprox/simple/images/index_gr_17.gif] using Mathematica™ function Plot3D.

  • [Graphics:Mathematica/LdeApprox/simple/images/index_gr_18.gif]

    [Graphics:Mathematica/LdeApprox/simple/images/index_gr_19.gif]

    [Graphics:Mathematica/LdeApprox/simple/images/index_gr_20.gif]
  • Comparing exact and approximate results for [Graphics:Mathematica/LdeApprox/simple/images/index_gr_21.gif] using Mathematica™ function Plot3D.

  • [Graphics:Mathematica/LdeApprox/simple/images/index_gr_22.gif]

    [Graphics:Mathematica/LdeApprox/simple/images/index_gr_23.gif]

    [Graphics:Mathematica/LdeApprox/simple/images/index_gr_24.gif]

    Note:

    This trivial example is just for Web. You can try more complex examples in your computer.