Application of Combined Modified Variational Iteration Method and Laplace Transform into Linear and Nonlinear Differential Equations

Abstract

In this research the variational iteration method is used for solving second-order initial value problems. The research discussed the use of this method to solve many important partial differential equations. This method is based on the use of Lagrange multipliers for identification of the optimal value of a parameter in a function. Also, this method solved many of the problems. The research has been in dealing with Laplace transform in ordinary differential equations and for solving integral equations and studying the variational iteration method (VIM) and Laplace transform, for the solution of certain classes of linear and nonlinear differential equations. The strategy is drafted and then illustrated through a number of test cases.

A combination of Laplace transform and modified variational iteration method are used to solve a new type of differential equation called convolution differential equations; it is possible to find the exact solutions or better approximate solutions of these equations. A based combined Laplace transform and the new modified variational iteration method is used to solve some nonlinear partial differential equations.

Application of a new method which is called Variational Iteration Perturbation Method ((VIPM)) is used. This method is a combination of the new integral “Variational Iteration” and the perturbation method to solve one dimensional fourth order parabolic linear partial differential equations with variable coefficients.