AD-FDSD for convection-diffusion problems

In this paper, alternating-direction method is combined with finite difference streamline-diffusion (FDSD) method to form an alternating-direction-FDSD procedure for two-dimensional nonlinear convection-dominated diffusion equations. Moreover, realisation of computation, analysis of stability and error estimation are presented. Numerical examples are also presented to demonstrate the method. Not only does this new method lower the dimension of solving two-dimensional nonlinear convection-diffusion equation, but it also keeps the stability and high accuracy of FDSD method.