The Homotopy Analysis Method to Solve the Modified Equal Width Wave Equation

Yusufoglu E., Selam C.

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, vol.26, no.6, pp.1434-1442, 2010 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 26 Issue: 6
  • Publication Date: 2010
  • Doi Number: 10.1002/num.20498
  • Journal Name: NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1434-1442
  • Keywords: auxiliary parameter, homotopy analysis method, modified equal-width wave equation, VARIATIONAL ITERATION METHOD, VISCOUS-FLOW PROBLEMS, APPROXIMATE SOLUTION, NONLINEAR EQUATIONS, NUMERICAL-SOLUTION, ANALYTIC SOLUTION, SOLITARY WAVES, HEAT-TRANSFER, GRADE FLUID, DIFFUSION
  • Anadolu University Affiliated: Yes

Abstract

In this article, to solve the modified equal width wave (MEW) equation, the homotopy analysis method (HAM) is proposed. The initial approximation can be freely chosen with possible unknown constant, which can be determined by using the boundary and initial conditions. The HAM contains the auxiliary parameter (h) over bar, which provides us to adjust and control the convergence region of solution series with a simple way. Three conservative quantities are reported. Numerical results show that this method is a promising and powerful tool to solve the MEW equation. (C) 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 26: 1434-1442, 2010