Solving Boussinesq-Like B(M,N) Equations Using Homotopy Analysis Method

Abstract

In this thesis, we have used the homotopy analysis method (HAM) to obtain approxi- mate analytical solutions of Boussinesq-like B(m, n) equations. The Homotopy Analy- sis Method is a mathematical technique used to solve nonlinear differential equations. This method employs the concept of the homotopy from topology to generate a con- vergent series solution for nonlinear equations. To assess the efficiency of the HAM, we conducted a comparative analysis between its results and the results obtained by the well-known numerical techniques(FDM). Two problems involving Boussinesq-like B(m,n) equations were considered to demonstrate the efficiency and effectiveness of the homotopy analysis method. The results were visualized through plotted graphs using matlab code.