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Improved Difference Scheme for a Singularly Perturbed Parabolic Reaction-Diffusion Equation with Discontinuous Initial Condition

  • Grigory Shishkin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5434)

Abstract

A Dirichlet problem is considered for a singularly perturbed parabolic reaction-diffusion equation with a piecewise-continuous initial condition. For this problem, using the method of additive splitting of singularities (generated by discontinuities of the initial function and its lowest derivatives) and the Richardson method, a finite difference scheme on piecewise-uniform meshes is constructed that converges ε-uniformly with the third and second order of accuracy in x and t, respectively.

Keywords

Initial Function Singular Component Grid Approximation Additive Splitting Richardson Scheme 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Grigory Shishkin
    • 1
  1. 1.Institute of Mathematics and MechanicsUral Branch of Russian Academy of SciencesEkaterinburgRussia

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