Abstract
This article treats of adaptive finite difference methods for the Dirichlet boundary value problems of Poisson-type equations on a sector or a disk. It is assumed that the exact solutions have singular derivatives on a part or the whole of the boundary. Some stretching functions are used to generate nonuniform grid points. It is then shown that, under some assumptions, the adaptive finite difference solutions are convergent and the convergence can be accelerated by varying parameters in the stretching functions. Numerical examples are given to illustrate how the accuracy of numerical solutions depends on the parameters.