Affiliations: [a] Department of Mathematics, King Khaild University, Saudi Arabia. E-mails: [email protected], [email protected] | [b] Department of Mathematics, King Abdulaziz University, Saudi Arabia. E-mail: [email protected]
Abstract: In this work, a comparative study of seven well-known mathematical techniques for the coupled Burgers’ equations is reported. The techniques involve in this comparison are as follows: Laplace transform Adomian decomposition method, Laplace transform homotopy perturbation method, Variational iteration method, Variational iteration decomposition method, Variational iteration homotopy perturbation method, the optimal homotopy asymptotic method, and OHAM with Daftardar–Jafari polynomial. Here we considered a practical example which consists of coupled Burgers’ equations with the kinematic viscosity ε=1. Convergence and stability analysis is a major part of this analysis. After a careful observation, it is found that the variational iteration method has faster convergence than all the remaining methods. Adomian decomposition method and Homotopy perturbation method show weaker stability in comparison with other involved techniques.
