ABSTRACT
This chapter considers the homotopy perturbation method (HPM), optimal homotopy asymptotic method (OHAM), and Haar wavelet method in order to compute the numerical solutions of the nonlinear system of partial differential equations like Boussinesq–Burgers' equations. In HPM and OHAM, the concept of homotopy from topology and the conventional perturbation technique were merged to propose a general analytic procedure for the solution of nonlinear problems. OHAM provides a simple and easy way to control and adjust the convergence region for strong nonlinearity. Unlike other homotopy procedures, OHAM ensures a very rapid convergence since it needs only two or three terms for achieving an accurate solution instead of an infinite series. An advantage of OHAM over perturbation methods is that it does not depend on small parameters. Various analytical methods such as the Darboux transformation method, Lax pair, and Backlund transformation method have been used in attempting to solve Boussinesq–Burgers' equations.
