IMPROVED VARIATIONAL ITERATION METHOD FOR THE SOLUTION OF INITIAL VALUE PROBLEMS

ABSTRACT

Numerous numbers of methods have been developed to solve various types of Initial Value Problems (IVPs). The desire to improve the acceleration of convergence is still a burning issue in the literature. This study is aimed at developing an Improved Variational Iteration Method (IVIM) that gives an approximate solution to linear and nonlinear IVPs so as to facilitate speedy evaluation. An implicit method is developed from the existing Variational Iteration Method (VIM), so that the Lagrange multiplier can be effectively obtained using Variational theory so as to facilitate the computational work and improve the solutions. Numerical experiments are carried out and comparative analyses with Variational Iteration Method are conducted. The approximate results generated by the newly developed method are in agreement with the analytic solutions and also the convergence rate of the new method to the analytic solutions is faster when compared to the existing VIM.