Application of variational iteration method to a general Riccati equation

Abstract

In this paper, the variational iteration method (VIM) is applied to the solution of general Riccati differential equations. The equations under consideration includes one with variable coefficient and one in matrix form. In VIM, a correction functional is constructed by a general Lagrange multiplier which can be identified via a variational theory. The VIM yields an approximate solution in the form of a quickly convergent series. Comparisons with exact solution and the fourth-order RungeKutta method show that the VIM is a powerful method for the solution of nonlinear equations. The present paper may be a suitable and fruitful exercise for teaching and better understanding techniques in advanced undergraduate courses on classical mechanics.