Variational Iteration Method - Chakraverty, Snehashish; Mahato, Nisha; Karunakar, Perumandla; Dilleswar Rao, Tharasi (Advanced Numerical and Semi-Analytical Methods for Differential Equations, 2019)
The variational iteration method (VIM) is one of the well‐known semi‐analytical methods for solving linear and nonlinear ordinary as well as partial differential equations. The main advantage of the method lies in its flexibility and ability to solve nonlinear equations easily. The method can be used in bounded and unbounded domains as well. By this method one can find the convergent successive approximations of the exact solution of the differential equations if such a solution exists. Wazwaz used the VIM for solving the linear and nonlinear Volterra integral and integro‐differential equations and explained clearly how to use this method for solving homogenous and inhomogeneous partial differential equations. This chapter solves few test problems using the present method to make the readers familiar with the method. As such, two linear nonhomogeneous partial differential equations are handled in two examples, and a nonlinear partial differential equation has been solved in other example.