A Numerical Approach to the Rosenau-KdV equation using Galerkin Cubic Finite Element Method

UÇAR Y., KARAAGAC B., KUTLUAY S.

INTERNATIONAL JOURNAL OF APPLIED MATHEMATICS & STATISTICS, cilt.56, sa.3, ss.83-92, 2017 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 56 Sayı: 3
  • Basım Tarihi: 2017
  • Dergi Adı: INTERNATIONAL JOURNAL OF APPLIED MATHEMATICS & STATISTICS
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), zbMATH
  • Sayfa Sayıları: ss.83-92
  • Anahtar Kelimeler: Galerkin finite element method, Rosenau-KdV equation, Runge-Kutta method, cubic B-spline, solitary wave, SOLITONS
  • İnönü Üniversitesi Adresli: Evet

Özet

In this paper, a Galerkin finite element method has been used to solve numerically the Rosenau-KdV equation using cubic B-spline functions. The system of ordinary differential equations obtained in terms of element parameters by the application of the method has been solved by using the fourth order Runge-Kutta method. The error norms L-2 and L-infinity together with invariants I-1 and I-2 have been calculated to show the accuracy and efficiency of the method. The computed results have been compared with exact values and also other numerical results available in the literature.