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.
