CONVERGENCE ANALYSIS OF EXPONENTIAL EXPANDING MESHES COMPACT-FDM FOR POISSON EQUATION IN POLAR COORDINATE SYSTEM

摘要

We develop a third (four) order accurate new nine-point compact finite difference scheme for the numerical solution of two-dimensional Poisson equation in polar form. The peculiar character of the exponential expanding mesh parameters help us in resolving interior or boundary layer in the partial differential equations. The proposed scheme takes care of grid singularity and oblique coefficient that accompany the polar form of Poisson equation. A detailed discrete convergence analysis for the difference scheme has been developed based on monotone and irreducible property of the iteration matrix. Numerical accuracy of the solutions has been obtained that shows the applicability of the scheme in the presence of singularity and thin layers. Comparing the proposed third order compact scheme with the corresponding fourth order uniform mesh strategy, the solution accuracy proved to be highly satisfactory.