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Application of homotopy perturbation method to the RLW and generalized modified Boussinesq equations. (English) Zbl 1203.65214

Summary: He’s homotopy perturbation method (HPM) is implemented for finding the solitary-wave solutions of the regularized long-wave (RLW) and generalized modified Boussinesq (GMB) equations. We obtain numerical solutions of these equations for the initial conditions. We will show that the convergence of the HPM is faster than those obtained by the Adomian decomposition method (ADM). The obtained solutions, in comparison with the exact solutions admit a remarkable accuracy. A clear conclusion can be drawn from the numerical results that the HPM provides highly accurate numerical solutions for nonlinear differential equations.

MSC:

65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
35Q53 KdV equations (Korteweg-de Vries equations)
35C05 Solutions to PDEs in closed form
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