Fourth-order compact schemes for the numerical simulation of coupled Burgers' equation

This paper introduces two new modified fourth-order exponential time differencing Runge Kutta (ETDRK) schemes in combination with a global fourth-order compact finite difference scheme (in space) for direct integration of nonlinear coupled viscous Burgers' equations in their original form without using any transformations or linearization techniques. One scheme is a modification of the Cox and Matthews ETDRK4 scheme based on (1, 3)-Pade approximation and other is a modification of Krogstad's ETDRK4-B scheme based on (2, 2)-Pade approximation. Efficient versions of the proposed schemes are obtained by using a partial fraction splitting technique of rational functions. The stability properties of the proposed schemes are studied by plotting the stability regions, which provide an explanation of their behavior for dispersive and dissipative problems. The order of convergence of the schemes is examined empirically and found that the modification of ETDRK4 converges with the expected rate e