ISSN 1 746-7233, England, UK World Journal of Modelling and Simulation Vol. 9 (2013) No. 3, pp. 173-180 Coupling of laplace transform and correction functional for wave equations Afshan Kanwal , Syed Tauseef Mohyud-Din * Department of Mathematics, HITEC University, Taxila Cantt, Pakistan (Received December 12 2012, Revised June 01 2013, Accepted July 07 2013) Abstract. In this paper, we apply Variational Iteration Method coupled with Laplace Transform Method to solve wave equations which arise very frequently in physical problems related to engineering and applied sciences. It is observed that the proposed technique is suitable for such problems and is very user-friendly. Several examples are given to re-confirm the efficiency of the suggested algorithm. Keywords: variational iteration method, laplace transform method, wave equations, MAPLE 13 1 Introduction The rapid development of nonlinear sciences [1–14] witnesses a wide range of analytical and numerical techniques by various scientists. Most of the developed schemes have their limitations like limited conver- gence, divergent results, linearization, discretization, unrealistic assumptions and non-compatibility with the versatility of physical problems [1–14] . The basic motivation of present study is the coupling of correction func- tional of Variational Iteration Method (VIM) and Laplace transform. It has been observed that the Coupling of Laplace Transform and Correction Functional enhances its efficiency and reduces the computational work to a tangible level. Moreover, this version is more user-friendly and it overcomes some of the basic deficiencies. The suggested algorithm is tested on linear, nonlinear wave equations and wave-like equations in bounded and unbounded domains. Numerical results are very encouraging. 2 Variational Iteration Method (VIM) To illustrate the basic concept of the He’s VIM, we consider the following general differential equation L[u]+ N [u]= g(x), (1) where L is a linear operator, N a nonlinear operator and g(x) is the inhomogeneous term. According to variational iteration method [2–4, 6–11, 14] , we can construct a correction functional as follows u n+1 (x)= u n (x)+ x  0 λ  Lu n (s)+ N ˜ u n (s) - g(s)  ds, (2) where λ is a Lagrange multiplier [2–4, 6–11, 14] , which can be identified optimally via variational iteration method. The subscripts n denote the nth approximation, ˜ u n is considered as a restricted variation. i.e. δ ˜ u n =0; Eq. (2) is called a correction functional. The solution of the linear problems can be solved in a single iteration step due to the exact identification of the Lagrange multiplier. The principles of variational iteration method * Corresponding author. E-mail address: syedtauseefs@hotmail.com. Published by World Academic Press, World Academic Union