The homotopy-perturbation method applied for solving complex-valued differential equations with strong cubic nonlinearity

In this paper the homotopy perturbation method is adopted for solving a complex-valued second-order strongly nonlinear differential equation. Homotopy with an imbedding parameter p E [0, 1] is constructed. The perturbation procedure with parameter p transforms the strongly nonlinear differential equation into a system of linear complex-valued differential equations whose solutions give the approximate solution of the initial differential equation. To illustrate the effectiveness and convenience of the suggested procedure, a Duffing equation with strong cubic nonlinearity is considered. The periodic solution in the first approximation is obtained. The solution is compared with the exact one and shows good agreement. (c) 2004 Elsevier Ltd. All rights reserved.