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.
Highlights
Open AccessThe Riccati equation plays a great role in blueprint and analysis the linear and nonlinear optimal control problems
HPM introduced by He [5], it can solve a large class of nonlinear problems activity, accurately and
We apply the VHPM to Riccati Equation (1), we start this method by applying HPM in Equation (8) on Equation (1), we get
Summary
The Riccati equation plays a great role in blueprint and analysis the linear and nonlinear optimal control problems. Numerical Solution of this equation has been acquired by applying Adomian’s decomposition method [1], homotopy. The application of HPM on nonlinear problems has been implemented by scientists and engineers, because this method is to continuously deform a difficult problem under study into a simple problem easy to solve. It is simple and powerful method for solving a broad type of nonlinear Problem. We end this paper by conclusion that reveal that these methods are very effective and convenient for solving nonlinear Riccati equations
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