Comparison between homotopy perturbation method and optimal homotopy asymptotic method for the soliton solutions of Boussinesq–Burger equations

• Optimal homotopy asymptotic method has been proposed for Boussinesq–Burger equation.
• In this paper soliton solutions of Boussinesq–Burger equation have been analyzed.
• The obtained results have been compared with HPM method solutions.
• The results reveal that the OHAM is very effective and simple.
• The numerical solutions are presented graphically in 3D surfaces and 2D plots.

In this article, a comparative study between homotopy perturbation method (HPM) and optimal homotopy asymptotic method (OHAM) is presented. Homotopy perturbation method is applied to compute the numerical solutions of non-linear partial differential equations like Boussinesq–Burger equations. The approximate solutions of the Boussinesq–Burger equation are compared with the optimal homotopy asymptotic method as well as with the exact solutions. Comparison between our solutions and the exact solution shows that both the methods are effective and accurate in solving nonlinear problems whereas OHAM is accurate with less number of iterations in compared to HPM. In OHAM the convergence region can be easily adjusted and controlled. OHAM provides a simple and easy way to control and adjust the convergence region for strong nonlinearity and is applicable to highly nonlinear fluid problem like Boussinesq–Burger equations.