Compact operator method of accuracy two in time and four in space for the numerical solution of coupled viscous Burgers' equations

In this paper, we propose a new two-level implicit compact operator method of order two in time (t) and four in space (x) for the solution of time dependent coupled viscous Burgers' equations. In this method, we did not use any transformation or linearization technique to handle nonlinearity. We use only 3-spatial grid points and the obtained tridiagonal nonlinear system has been solved by Newton's iterative method. The test problems considered in the literature have been discussed to demonstrate the strength and utility of the proposed method. The computed numerical solutions are in good agreement with the exact solutions and competent with those available in earlier studies. We show that the proposed method enables us to obtain high accurate solution for high Reynolds number.