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The application of the homotopy perturbation method and the homotopy analysis method to the generalized Zakharov equations. (English) Zbl 1246.65193

Summary: We introduce two powerful methods to solve the generalized Zakharov (GZ) equations; one is the homotopy perturbation method (HPM) and the other is the homotopy analysis method (HAM). The homotopy perturbation method is proposed for solving the generalized Zakharov equations. The initial approximations can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions; the homotopy analysis method is applied to solve the generalized Zakharov equations. HAM is a strong and easy-to-use analytic tool for nonlinear problems. Computation of the absolute errors between the exact solutions of the GZ equations and the approximate solutions, comparison of the HPM results with those of Adomian’s decomposition method and the HAM results, and computation the absolute errors between the exact solutions of the GZ equations with the HPM solutions and HAM solutions are presented.

MSC:

65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
35Q53 KdV equations (Korteweg-de Vries equations)
35Q35 PDEs in connection with fluid mechanics
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
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