A Solution of Riccati Nonlinear Differential Equation using Enhanced Homotopy Perturbation Method (EHPM)

Abstract

Homotopy Perturbation Method is an effective method to find a solution of a nonlinear differential equation, subjected to a set of boundary condition. In this method a nonlinear and complex differential equation is transformed to series of linear and nonlinear and almost simpler differential equations. These set of equations are then solved secularly. Finally a linear combination of the solutions completes the answer if the convergence is maintained. HPM based solution incorporates some reasonable assumptions. These are inspired from the boundary condition and a separation mechanism. In this paper, the need for stability verification is shown trough some examples. The novel idea is to keep the inherent stability of nonlinear dynamic in whole term, even if the selected linear part is not stable. Consequently, HPM is enhanced by a preliminary assumption. The proposed method is applied to Riccati equation as well as some other problems. The simulation result verifies the significance of the method whilst numerical and the exact solutions confirm the achievement.