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A Multicomponent Alternating Direction Method for Numerical Solution of Boussinesq Paradigm Equation

  • Natalia Kolkovska
  • Krassimir Angelow
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8236)

Abstract

We construct and analyze a multicomponent alternating direction method (a vector additive scheme) for the numerical solution of the multidimensional Boussinesq Paradigm Equation (BPE). In contrast to the standard splitting methods at every time level a system of many finite difference schemes is solved. Thus, a vector of the discrete solutions to these schemes is found. It is proved that these discrete solutions converge to the continuous solution in the uniform mesh norm with O(|h|2 + τ) order. The method provides full approximation to BPE and is efficient in implementation. The numerical rate of convergence and the altitudes of the crests of the traveling waves are evaluated.

Keywords

Boussinesq Equation multicomponent ADI method vector additive scheme Sobolev type problem 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Natalia Kolkovska
    • 1
  • Krassimir Angelow
    • 1
  1. 1.Institute of Mathematics and InformaticsBulgarian Academy of SciencesSofiaBulgaria

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