The meshless kernel-based method of lines for solving the equal width equation

DERELİ Y., Schaback R.

APPLIED MATHEMATICS AND COMPUTATION, vol.219, no.10, pp.5224-5232, 2013 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 219 Issue: 10
  • Publication Date: 2013
  • Doi Number: 10.1016/j.amc.2012.10.086
  • Journal Name: APPLIED MATHEMATICS AND COMPUTATION
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.5224-5232
  • Keywords: Radial basis functions, Solitons, Nonlinear ODEs, WAVE-EQUATION, UNDULAR BORE
  • Anadolu University Affiliated: Yes

Abstract

The Equal Width equation governs nonlinear wave phenomena like waves in shallow water. Here, it is solved numerically by the Method of Lines using a somewhat unusual setup. There is no linearization of the nonlinear terms, no error in handling the starting approximation, and there are boundary conditions only at infinity. To achieve a space discretization of high accuracy with only few trial functions, meshless translates of radial kernels are used. In the numerical examples, the motion of solitary waves, the interaction of two and three solitary waves, the generation of wave undulation, the Maxwell initial condition, and the clash of two colliding solitary waves are simulated. Our numerical results compare favourably with results of earlier papers using other techniques. (C) 2012 Elsevier Inc. All rights reserved.