Variational Homotopy Perturbation Method for Solving Riccati Type Differential Problems

Abstract

In this paper, a Variational homotopy perturbation method is proposed to solve nonlinear Riccati differential equation. By combining the Variational Iteration Method and the Homotopy Perturbation Method, this technique possesses a fast convergence rate with high accuracy. The results reveal that the proposed method is very effective and simple.

Variational homotopy perturbation method for solving Lane-Emden initial value problems

“…In this paper, we will present a method based on combining the VIM and HPM, the Variational Homotopy Perturbation Method (VHPM) is proposed to solve many kinds of differential equations, for example, Bratu-Type Problems [1], Riccati Differential Problems [12] and Stiff Systems of ODEs [11]. Also, VHPM was applied on partial differential equations such as Fisher's Equation [21], Burgers' equations [9], Klein-Gordon and sine-Gordon equations [25].…”