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Ismail, M.S. (2009) Numerical Solution of a Coupled Korteweg-de Vries Equations by Collocation Method. Numerical Methods for Partial Differential Equations, 25, 275-291.
https://doi.org/10.1002/num.20343

has been cited by the following article:

• TITLE: Numerical Simulation of Modified Kortweg-de Vries Equation by Linearized Implicit Schemes

  AUTHORS: M. S. Ismail, Fakhirah Alotaibi

  KEYWORDS: MKdV Equation, Pade Approximation, Nonlinear Numerical Schemes, Linearly Implicit Schemes, Fixed Point Method, Interaction of Solitons

  JOURNAL NAME: Applied Mathematics, Vol.11 No.11, November 17, 2020

  ABSTRACT: In this paper, we are going to derive four numerical methods for solving the Modified Kortweg-de Vries (MKdV) equation using fourth Pade approximation for space direction and Crank Nicolson in the time direction. Two nonlinear schemes and two linearized schemes are presented. All resulting schemes will be analyzed for accuracy and stability. The exact solution and the conserved quantities are used to highlight the efficiency and the robustness of the proposed schemes. Interaction of two and three solitons will be also conducted. The numerical results show that the interaction behavior is elastic and the conserved quantities are conserved exactly, and this is a good indication of the reliability of the schemes which we derived. A comparison with some existing is presented as well.