2017-07-17

In this thesis, we study Variable-Coefficient Variant Boussinesq System, which describes the nonlinear and dispersive long gravity waves in shallow water traveling in two horizontal directions with varying depth. We solve the system numerically by using Adomian Decomposition Method, Adomian-Padé Technique, Variational Iteration Method, Modified Variational Iteration Method and Homotopy Analysis Method. We solve an example using the above methods to see which methods are suitable for this kind of nonlinear partial systems and which is more accurate and efficient than the others.