An Unconventional Finite Difference Scheme for Modified Korteweg-de Vries Equation

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KÖROĞLU C., AYDIN A.

ADVANCES IN MATHEMATICAL PHYSICS, vol.2017, 2017 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 2017
  • Publication Date: 2017
  • Doi Number: 10.1155/2017/4796070
  • Journal Name: ADVANCES IN MATHEMATICAL PHYSICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Hacettepe University Affiliated: Yes

Abstract

A numerical solution of the modified Korteweg-de Vries (MKdV) equation is presented by using a nonstandard finite difference (NSFD) scheme with theta method which includes the implicit Euler and a Crank-Nicolson type discretization. Local truncation error of the NSFD scheme and linear stability analysis are discussed. To test the accuracy and efficiency of the method, some numerical examples are given. The numerical results of NSFD scheme are compared with the exact solution and a standard finite difference scheme. The numerical results illustrate that the NSFD scheme is a robust numerical tool for the numerical integration of the MKdV equation.