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A New Approach for Numerical Solution of Modified Korteweg-de Vries Equation

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An Erratum to this article was published on 03 May 2017

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Abstract

In this paper, a lumped Galerkin method is applied with cubic B-spline interpolation functions to find the numerical solution of the modified Korteweg-de Vries (mKdV) equation. Test problems including motion of single solitary wave, interaction of two solitons, interaction of three solitons, and evolution of solitons are solved to verify the proposed method by calculating the error norms \(L_{2}\) and \(L_{\infty }\) and the conserved quantities mass, momentum and energy. Applying the von-Neumann stability analysis, the proposed method is shown to be unconditionally stable. Consequently, the obtained results are found to be harmony with the some recent results.

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  • 03 May 2017

    An erratum to this article has been published.

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Acknowledgements

The author, Turgut Ak, is grateful to The Scientific and Technological Research Council of Turkey for granting scholarship for Ph.D. studies.

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Authors and Affiliations

  1. Department of Transportation Engineering, Faculty of Engineering, Yalova University, 77100, Yalova, Turkey

    Turgut Ak

  2. Department of Mathematics, Faculty of Science and Art, Nevsehir Haci Bektas Veli University, 50300, Nevsehir, Turkey

    S. Battal Gazi Karakoc

  3. Department of Mathematical Sciences, Delaware State University, Dover, DE, 19901-2277, USA

    Anjan Biswas

  4. Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    Anjan Biswas

Authors
  1. Turgut Ak
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  2. S. Battal Gazi Karakoc
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  3. Anjan Biswas
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Correspondence to Turgut Ak.

Additional information

An erratum to this article is available at https://doi.org/10.1007/s40995-017-0245-6.

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Ak, T., Karakoc, S.B.G. & Biswas, A. A New Approach for Numerical Solution of Modified Korteweg-de Vries Equation. Iran J Sci Technol Trans Sci 41, 1109–1121 (2017). https://doi.org/10.1007/s40995-017-0238-5

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  • DOI: https://doi.org/10.1007/s40995-017-0238-5

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