Second Order Scheme For Korteweg-De Vries (KDV) Equation

Authors

  • Khandaker Md Eusha Bin Hafiz Department of Mathematics, Jahangirnagar University, Dhaka, Bangladesh
  • Laek Sazzad Andallah Department of Mathematics, Jahangirnagar University, Dhaka, Bangladesh

DOI:

https://doi.org/10.3329/jbas.v43i1.42237

Keywords:

KdV Equation, Soliton, Solitary Wave, Finite Difference Scheme

Abstract

The kinematics of the solitary waves is formed by Korteweg-de Vries (KdV) equation. In this paper, a third order general form of the KdV equation with convection and dispersion terms is considered. Explicit finite difference schemes for the numerical solution of the KdV equation is investigated and stability condition for a first-order scheme using convex combination method is determined. Von Neumann stability analysis is performed to determine the stability condition for a second order scheme. The well-known qualitative behavior of the KdV equation is verified and error estimation for comparisons is performed.

Journal of Bangladesh Academy of Sciences, Vol. 43, No. 1, 85-93, 2019

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Published

2019-07-16

How to Cite

Hafiz, K. M. E. B., & Andallah, L. S. (2019). Second Order Scheme For Korteweg-De Vries (KDV) Equation. Journal of Bangladesh Academy of Sciences, 43(1), 85–93. https://doi.org/10.3329/jbas.v43i1.42237

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