Variational iteration method for differential

Abstract

The variational iteration method (VIM) is a powerful method for solving a wide class of linear and nonlinear problems, first introduced by the Chinese mathematician He in 1999. This method is based on the use of Lagrange multiplier for evaluation of optimal value for parameters in a correction functional. The VIM has successfully been applied for a wide variety of scientific and engineering applications. This thesis is concerned with the VIM for both ordinary and partial differential equations. Firstly, we present a brief introduction for the theory of calculus of variation, then the VIM is applied for ordinary differential equations. We consider both linear and nonlinear equations. In addition, a convergent analysis for a specific class of the differential equations is examined. Furthermore, the VIM is applied to solve linear as well as nonlinear partial differential equations. In particular, the Laplace transform is used with the VIM to solve a class of partial differential equations.