Applications on Hybrid VIM Methods

Abstract

This research examines the Analytical Approximate Solutions of the Non Linear Partial Differential Equations such as Non Linear Wave Equations, In viscid and Viscid Burgers’ Equations etc. using Variational Iteration Method (VIM) and hybrid VIM methods such as Variational Iteration Adomian Decomposition Method (VIADM), New Modified Kamal Variational Iteration Adomian Decomposition Method (New MKVIADM), Laplace Variational Iteration Method (LVIM), Modified Variational Iteration Laplace Transform Method (MVILTM) etc. VIM is a powerful tool to solve the differential equations which gives fast consecutive approximations without using any conditional assumptions or any further transformations which may change the physical behavior of the problem. Adomian Decomposition method is also an efficient method which handles the linear and non linear differential and integral equations with Initial and Boundary Conditions. It provides an efficient numerical solution in the form of an infinite series which is obtained iteratively. It usually converges to the exact solution using Adomian polynomials. Laplace Transform is a very popular and powerful integral transform to solve the linear initial value problems. Kamal Transform is a recent new arrival of an integral transform which is commanding to solve the linear initial value problems. To solve the equations the combination of the methods has been used and tried to implement it to solve the Non Linear Partial Differential Equations. Aim of this research is to check the influence and accurateness of hybrid VIM methods. To exemplify the reliability of the methods, we made the comparison of the solutions with different methods. The obtained results declare that this alternative approach converges rapidly, helps for getting the accuracy, and handles the ones with discontinuities.