Variational Iteration Method

Abstract

Differential equations are encountered in various fields such as physics, chemistry, biology, mathematics and engineering. Most nonlinear models of real-life problems are still very difficult to solve either numerically or theoretically. Many unrealistic assumptions have to be made to make nonlinear models solvable. There has recently been much attention devoted to the search for better and more efficient solution methods for determining a solution, approximate or exact, analytical or numerical, to nonlinear models. Finding exact/approximate solutions of these nonlinear equations are interesting and important. One of these methods is variational iteration method (VIM), which has been proposed by Ji-Huan He in 1997 based on the general Lagrange’s multiplier method. The main feature of the method is that the solution of the linearized problem is used as the initial approximation for the linear and nonlinear problems. Then a more highly precise approximation at some special point can be obtained. This approximation converges rapidly to an accurate solution. VIM is very powerful and efficient in finding analytical as well as numerical solutions for a wide class of differential equation