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

Bashan A., YAĞMURLU N. M., UÇAR Y., ESEN A.

INTERNATIONAL JOURNAL OF MODERN PHYSICS C, cilt.29, sa.6, 2018 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 29 Sayı: 6
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1142/s0129183118500432
  • Dergi Adı: INTERNATIONAL JOURNAL OF MODERN PHYSICS C
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: Partial diffferential equations, differential quadrature method, cmKdV equation, solitary waves, modified cubic B-splines., DE-VRIES EQUATION, WAVES, KDV
  • İnönü Üniversitesi Adresli: Evet

Özet

In the present paper, a novel perspective fundamentally focused on the differential quadrature method using modifi ed 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 effciency 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-infinity will be calculated for single solitary wave solutions to measure the effciency and the accuracy of the present approach. Meanwhile, the three lowest conservation quantities will be calculated and also used to test the effciency 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 effcient one for solving the cmKdV equation and can also be used for numerical solutions of other problems.