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

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  • Canan Koroglu
  • Ayhan Aydin

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.

Suggested Citation

  • Canan Koroglu & Ayhan Aydin, 2017. "An Unconventional Finite Difference Scheme for Modified Korteweg‐de Vries Equation," Advances in Mathematical Physics, John Wiley & Sons, vol. 2017(1).
    • Handle: RePEc:wly:jnlamp:v:2017:y:2017:i:1:n:4796070
    DOI: 10.1155/2017/4796070
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    References listed on IDEAS

    as
    1. Lei Zhang & Lisha Wang & Xiaohua Ding, 2014. "Exact Finite Difference Scheme and Nonstandard Finite Difference Scheme for Burgers and Burgers-Fisher Equations," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-12, January.
    2. Cuicui Liao & Xiaohua Ding, 2012. "Nonstandard Finite Difference Variational Integrators for Multisymplectic PDEs," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-22, November.
    3. Cuicui Liao & Xiaohua Ding, 2012. "Nonstandard Finite Difference Variational Integrators for Multisymplectic PDEs," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    4. Lei Zhang & Lisha Wang & Xiaohua Ding, 2014. "Exact Finite Difference Scheme and Nonstandard Finite Difference Scheme for Burgers and Burgers‐Fisher Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
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