Solution of Nonlinear Boussinesq Equations By Modified Adomian Decomposition Method

Abstract

The application of Adomian’s decomposition method and its modifications to partial differential equations, when the exact solution is not reached, demands the use of truncated series. But the solution’s series may have small convergence radius and the truncated series may be inaccurate in many regions. In order to enlarge the convergence domain of the truncated series, Pad´e approximants technique is applied to partial differential equations, particularly to Boussinesq equations to find explicit and travelling waves solutions. Graphical illustrations were used to show that this technique can enlarge the domain of convergence of Adomian’s solution. It is also showed that the solution accuracy can be improved by increasing the order of the Pad´e approximants. In this thesis, besides graphical illustrations, also numerical results are presented to show that this technique can not only enlarge the domain of convergence of the solution but also improves its accuracy even when the actual solution cannot be expressed as the ratio of two polynomials.