The improved backward substitution method for the simulation of time-dependent nonlinear coupled Burgers' equations

In this paper, we make the first attempt to extend the improved backward substitution method for solving unsteady nonlinear coupled Burgers' equations. The temporal variable is discretized by the Crank-Nicolson finite difference scheme. Then the improved backward substitution method is applied to solve the corresponding system. The solution to the discretized system is approximated by the primary approximation which is obtained from the boundary condition and its corresponding correcting solution. A simple iteration scheme is used to eliminate the non-linearity of considered problems. To illustrate the accuracy and efficiency, we consider five examples and results are compared with existing results in literatures. Numerical experiments demonstrate that the present method has potential for real engineering problems.