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A Numerical Solution for Hirota-Satsuma Coupled KdV Equation

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  • M. S. Ismail
  • H. A. Ashi

Abstract

A Petrov-Galerkin method and product approximation technique are used to solve numerically the Hirota-Satsuma coupled Korteweg-de Vries equation, using cubic -splines as test functions and a linear -spline as trial functions. The implicit midpoint rule is used to advance the solution in time. Newton’s method is used to solve the block nonlinear pentadiagonal system we have obtained. The resulting schemes are of second order accuracy in both directions, space and time. The von Neumann stability analysis of the schemes shows that the two schemes are unconditionally stable. The single soliton solution and the conserved quantities are used to assess the accuracy and to show the robustness of the schemes. The interaction of two solitons, three solitons, and birth of solitons is also discussed.

Suggested Citation

  • M. S. Ismail & H. A. Ashi, 2014. "A Numerical Solution for Hirota-Satsuma Coupled KdV Equation," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-9, August.
    • Handle: RePEc:hin:jnlaaa:819367
    DOI: 10.1155/2014/819367
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    Cited by:

    1. Başhan, Ali, 2019. "A mixed algorithm for numerical computation of soliton solutions of the coupled KdV equation: Finite difference method and differential quadrature method," Applied Mathematics and Computation, Elsevier, vol. 360(C), pages 42-57.

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