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Highly efficient approach to numerical solutions of two different forms of the modified Kawahara equation via contribution of two effective methods

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  • Başhan, Ali

Abstract

The numerical solutions of the two different forms of the modified Kawahara equation namely bell-shaped soliton solutions and travelling wave solutions that occur thereby the different form of the KdV equation have been investigated. To improve the numerical solutions, two efficient methods have been used together. Firstly, Crank–Nicolson discretization algorithm for time integration is used and then fifth-order quintic B-spline based differential quadrature method for space integration is used. To observe the performance of the present algorithm bell-shaped soliton solution and travelling wave solutions are surveyed. The error norms L2 and L∞ are obtained quite less than earlier papers. The invariants and relative changes of invariants are added to sympathize with superior present results.

Suggested Citation

  • Başhan, Ali, 2021. "Highly efficient approach to numerical solutions of two different forms of the modified Kawahara equation via contribution of two effective methods," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 179(C), pages 111-125.
    • Handle: RePEc:eee:matcom:v:179:y:2021:i:c:p:111-125
    DOI: 10.1016/j.matcom.2020.08.005
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    References listed on IDEAS

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    1. 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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