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Advances in Mathematical Physics
Volume 2017, Article ID 4796070, 9 pages
https://doi.org/10.1155/2017/4796070
Research Article

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

1Mathematics Department, Science Faculty, Hacettepe University, Beytepe, 06800 Ankara, Turkey
2Mathematics Department, Atilim University, Incek, 06830 Ankara, Turkey

Correspondence should be addressed to Canan Koroglu; rt.ude.epettecah@ulgorokc

Received 25 July 2017; Accepted 9 October 2017; Published 1 November 2017

Academic Editor: Ming Mei

Copyright © 2017 Canan Koroglu and Ayhan Aydin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.