Paper Title
A Backward Semi-Lagrangian Scheme for Coupled Burgers' Equation

This paper is intended as an application of backward semi-Lagrangian scheme combined with the error correction method to obtain numerical solutions for nonlinear coupled Burgers' equation. To linearize the nonlinear diffusion-reaction system resulted from the backward semi-Lagrangian process, we develop a type of extrapolation scheme without the damaging of temporal accuracy. Through the numerical simulations of the targeted equations, we demonstrate the proposed method has the second-order convergence rates in time and space. In addition, our numerical results are in good agreement with the analytic solution and offer better accuracy in comparison with other existing scheme. Key word- Backward semi-Lagrangian method; Error correction method; Time dependent nonlinear partial differential equation; Coupled Burgers' equation