Fourth-order optimal iterative schemes for convection-diffusion equation

Successive overrelaxation schemes along with their scope are presented for the one-dimensional convection-diffusion equation with a small diffusion coefficient. Optimum relaxation parameters are derived analytically for these schemes developed by approximating the derivatives in the equation using the compact fourth-order differences. The solutions are compared with the widely used central difference solutions and are found to be both oscillation-free and convergent for all cell Reynolds numbers. Numerical experiments carried out on the schemes supplement the analytical results.