A new perspective for the numerical solutions of the cmKdV equation via modified cubic B-spline differential quadrature method
Küçük Resim Yok
Tarih
2018
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
World Scientific Publ Co Pte Ltd
Erişim Hakkı
info:eu-repo/semantics/closedAccess
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.
Açıklama
Anahtar Kelimeler
Partial diffferential equations, differential quadrature method, cmKdV equation, solitary waves, modified cubic B-splines.
Kaynak
International Journal of Modern Physics C
WoS Q Değeri
Q3
Scopus Q Değeri
Q3
Cilt
29
Sayı
6