Analytical Approximate Solutions of Non Linear Partial Differential Equations using VIM, VIADM and New Modified KVIADM

Abstract

This paper examines the Analytical Approximate Solutions of the Non Linear Partial Differential Equations such as Non Linear Wave Equations and In viscid Burgers’ Equation using Variational Iteration Method (VIM), Variational Iteration Adomian Decomposition Method (VIADM) and New Modified Kamal Variational Iteration Adomian Decomposition Method (New MKVIADM). VIM is a powerful tool to solve the differential equations which gives fast consecutive approximations without any conditional assumptions or any further transformations which may change the physical behaviour 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. Kamal Transform is a very recent new arrival of an integral transform which is commanding to solve the linear initial value problems. To check the efficiency of these methods, we have illustrated two non linear wave equations and one In Viscid Burgers’ equation. Objective of this paper is that, how rapidly these methods converge to the exact solution in the closed form, in the given domain for the given initial conditions, and still how it sustains the high accuracy and precision. Our aim in this paper is try to employ the combination of three different kinds of methods. The strategy of the methods is outlined and in view of the convergence of the methods and to show how it fulfils the objectives.