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In this paper, the modified homotopy perturbation method is applied for analytical treatment of differential equations. The modified HPM yields an analytical solution in terms of a rapidly convergent infinite power series with easily computable terms. The efficiency of the modified technique is examined by several illustrative examples. In all cases of differential equations, the modified HPM yields the exact solutions in two iterations only.

In this paper, the homotopy-perturbation method (HPM) proposed by J.-H. He is adopted for solving linear and nonlinear systems of partial differential equations (PDEs). In this method, a homotopy parameter p, which takes the values from 0 to 1, is introduced. When p = 0, the system of equations usually reduces to a sufficiently simplified form, which normally admits a rather simple solution. As p gradually increases to 1, the system goes through a sequence of 'deformations', the solution of each of which is 'close' to that at the previous stage of 'deformation'. Eventually at p = 1, the system takes the original form of the equation and the final stage of 'deformation' gives the desired solution. Some examples are presented to demonstrate the efficiency and simplicity of the method.