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A mixed algorithm for numerical computation of soliton solutions of the coupled KdV equation: Finite difference method and differential quadrature method

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  • Başhan, Ali

Abstract

The aim of the manuscript is to investigate numerical solutions of the system of coupled Korteweg-de Vries equation. For this approximation, we have used finite difference method for time integration and differential quadrature method depending on modified cubic B-splines for space integration. To display the accuracy of the present mixed method three famous test problems namely single soliton, interaction of two solitons and birth of solitons are solved and the error norms L2 and L∞ are computed and compared with earlier works. Comparison of error norms show that present mixed method obtained superior results than earlier works by using same parameters and less number of nodal points. At the same time, two lowest invariants and amplitude values of solitons during the simulations are calculated and reported. In addition those, relative changes of invariants are computed and tabulated. Properties of solitons observed clearly at the all of the test problems and figures of the all of the simulations are given.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:360:y:2019:i:c:p:42-57
    DOI: 10.1016/j.amc.2019.04.073
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    References listed on IDEAS

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    1. 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.
    2. Assas, Laila M.B., 2008. "Variational iteration method for solving coupled-KdV equations," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 1225-1228.
    3. Ali Başhan & N. Murat Yağmurlu & Yusuf Uçar & Alaattin Esen, 2018. "A new perspective for the numerical solutions of the cmKdV equation via modified cubic B-spline differential quadrature method," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 29(06), pages 1-17, June.
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