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A new perspective for the numerical solutions of the cmKdV equation via modified cubic B-spline differential quadrature method

Author

Listed:
  • Ali Başhan

    (Department of Mathematics, Faculty of Science and Art, Bulent Ecevit University, Zonguldak 67100, Turkey)

  • N. Murat Yağmurlu

    (Department of Mathematics, Faculty of Science and Art, Inonu University, Malatya 44200, Turkey)

  • Yusuf Uçar

    (Department of Mathematics, Faculty of Science and Art, Inonu University, Malatya 44200, Turkey)

  • Alaattin Esen

    (Department of Mathematics, Faculty of Science and Art, Inonu University, Malatya 44200, Turkey)

Abstract

In the present paper, a novel perspective fundamentally focused on the differential quadrature method using modified cubic B-spline basis functions are going to be applied for obtaining the numerical solutions of the complex modified Korteweg–de Vries (cmKdV) equation. In order to test the effectiveness and efficiency of the present approach, three test problems, that is single solitary wave, interaction of two solitary waves and interaction of three solitary waves will be handled. Furthermore, the maximum error norm L∞ will be calculated for single solitary wave solutions to measure the efficiency and the accuracy of the present approach. Meanwhile, the three lowest conservation quantities will be calculated and also used to test the efficiency of the method. In addition to these test tools, relative changes of the invariants will be calculated and presented. In the end of these processes, those newly obtained numerical results will be compared with those of some of the published papers. As a conclusion, it can be said that the present approach is an effective and efficient one for solving the cmKdV equation and can also be used for numerical solutions of other problems.

Suggested Citation

  • Ali Başhan & N. Murat Yağmurlu & Yusuf Uçar & Alaattin Esen, 2018. "A new perspective for the numerical solutions of the cmKdV equation via modified cubic B-spline differential quadrature method," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 29(06), pages 1-17, June.
    • Handle: RePEc:wsi:ijmpcx:v:29:y:2018:i:06:n:s0129183118500432
    DOI: 10.1142/S0129183118500432
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