Two efficient numerical methods for solving Rosenau-KdV-RLW equation

ÖZER S.

KUWAIT JOURNAL OF SCIENCE, cilt.48, sa.1, ss.14-24, 2021 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 48 Sayı: 1
  • Basım Tarihi: 2021
  • Doi Numarası: 10.48129/kjs.v48i1.8610
  • Dergi Adı: KUWAIT JOURNAL OF SCIENCE
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Arab World Research Source, zbMATH
  • Sayfa Sayıları: ss.14-24
  • Anahtar Kelimeler: Cubic B-spline functions, Galerkin method, Rosenau-KdV-RLW, Strang time-splitting, FINITE-DIFFERENCE SCHEME, SHOCK-WAVES, CONVERGENCE, SOLITONS
  • İnönü Üniversitesi Adresli: Evet

Özet

In this study, two efficient numerical schemes based on B-spline finite element method (FEM) and time-splitting methods for solving Rosenau-KdV-RLW equation are presented. In the first method, the equation is solved by cubic B-spline Galerkin FEM. For the second method, after splitting Rosenau-KdV-RLW equation in time, it is solved by Strang timesplitting technique using cubic B-spline Galerkin FEM. The differential equation system in the methods is solved by the fourth-order Runge-Kutta method. The stability analysis of the methods is performed. Both methods are applied to an example. The obtained numerical results are compared with some methods available in the literature via the error norms L-2 and L-infinity, convergence rates, and mass and energy conservation constants. The present results are found to be consistent with the compared ones.