An iteration free backward semi-lagrangian method for coupled burgers’ equations

In this paper, we develop a backward semi-Lagrangian method for solving the coupled Burgers’ equation. The main difficulty in the backward semi-Lagrangian method for this problem is treating the nonlinearity in the diffusion-reaction type equation, which has a reaction coefficient that is given in terms of coupled partial derivatives. To handle this difficulty, we proposed a new strategy using an extrapolation technique to split the nonlinearity into two diffusion-reaction boundary value problems, which are then solved in turn. In addition, we demonstrated the numerical accuracy and efficiency of the present method by comparing the numerical results with analytical solutions, or other existing numerical solutions that use alternate methods. In addition, we numerically proved that the proposed method exhibits second-order temporal convergence and fourth-order spatial convergence.