Finite Difference Approximations and Their Stencil Forms of Poisson's Equation in Cylindrical Coordinates.
NAVAL RESEARCH LAB WASHINGTON D C
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A systematic method is presented for finding finite difference approximations and their stencil representation of Poisson type second order partial differential equations in two variables for the purpose of obtaining accurate numerical solutions of these equations. The method uses a Taylor series expansion for the unknown function and its relationship to the known source function. The case of cylindrical coordinates with rectangular meshes is emphasized. Two known and two new stencils are presented. Modifications to stencils adjacent to physical boundaries are considered.
- Numerical Mathematics