Discrete singular convolution for the generalized variable-coefficient Korteweg-de Vries equation

Eben Maré, Jules Clement Mba, Edson Pindza

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

Numerical solutions of the generalized variable-coefficient Korteweg-de Vries equation are obtained using a discrete singular convolution and a fourth order singly diagonally implicit Runge-Kutta method for space and time discretisation, respectively. The theoretical convergence of the proposed method is rigorously investigated. Test problems including propagation of single solitons and interaction of solitary waves are performed to verify the efficiency and accuracy of the method. The numerical results are checked against available analytical solutions and compared with the Sinc numerical method. We find that our approach is a very accurate, efficient and reliable method for solving nonlinear partial differential equations.

Original languageEnglish
Pages (from-to)225-244
Number of pages20
JournalQuaestiones Mathematicae
Volume40
Issue number2
DOIs
Publication statusPublished - 3 Apr 2017

Keywords

  • Generalized Korteweg-de Vries equations
  • discrete singular convolution
  • exponential time differencing methods
  • soliton solutions

ASJC Scopus subject areas

  • Mathematics (miscellaneous)

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