Explicit Solutions of Helmholtz Equation and Fifth-order KdV Equation using Homotopy Perturbation Method

摘要

In this article, He's homotopy perturbation method (HPM), which does not need small parameter in the equation, is implemented to solve the linear Helmholtz partial differential equation and some nonlinear fifth-order Korteweg-de Vries (FKdV) partial differential equations with specified initial conditions. The initial approximations can be freely chosen with possible unknown constants which can be determined by imposing the boundary or initial conditions after few iterations. Comparison of the results with those obtained by Adomian's decomposition method reveals that HPM is very effective, convenient and quite accurate to both linear and nonlinear problems. It is predicted that HPM can be widely applied in engineering.