EFFECTS OF STRETCHING FUNCTIONS ON NON-UNIFORM FDM FOR POISSON-TYPE EQUATIONS ON A DISK WITH SINGULAR SOLUTIONS

摘要

In this paper, we consider the Dirichlet boundary value problem of Poisson type equations on a disk. We assume that the exact solution performs singular properties that its derivatives go to infinity at the boundary of the disk. A stretching polynomial-like function with a parameter is used to construct local grid refinements and the Swartztrauber-Sweet scheme is considered over the non-uniform partition. The effects of the parameter are analyzed completely by numerical experiments, which show that there exists an optimal value for the parameter to have a best approximate solution. Moreover, we show that the discrete system can be considered as a stable one by exploring the concept of the effective condition number.