Numerical solutions of the GEW equation using MLS collocation method

KAPLAN A. G., DERELİ Y.

INTERNATIONAL JOURNAL OF MODERN PHYSICS C, vol.28, no.1, 2017 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 28 Issue: 1
  • Publication Date: 2017
  • Doi Number: 10.1142/s0129183117500115
  • Journal Name: INTERNATIONAL JOURNAL OF MODERN PHYSICS C
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: Moving least squares collocation method, EW equation, MEW equation, GEW equation, EQUAL WIDTH EQUATION, LUMPED GALERKIN METHOD, RADIAL BASIS FUNCTIONS, WAVE-EQUATION, SOLITARY WAVES, MESHLESS METHOD, EW EQUATION
  • Anadolu University Affiliated: Yes

Abstract

In this paper, the generalized equal width wave (GEW) equation is solved by using moving least squares collocation (MLSC) method. To test the accuracy of the method some numerical experiments are presented. The motion of single solitary waves, the interaction of two solitary waves and the Maxwellian initial condition problems are chosen as test problems. For the single solitary wave motion whose analytical solution was known L-2, L-infinity error norms and pointwise rates of convergence were calculated. Also mass, energy and momentum invariants were calculated for every test problems. Obtained numerical results are compared with some earlier works. It is seen that the method is very efficient and reliable due to obtained numerical results are very satisfactorily. Stability analysis of dirfference equation was done by applying the moving least squares collocation method for GEW equation.