Finite Difference Approximations and Their Stencil Forms of Poisson's Equation in Cylindrical Coordinates.

Abstract

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.

Document Details

Document Type
Technical Report
Publication Date
May 01, 1975
Accession Number
ADA011816

Entities

People

  • John G. Siambis
  • Roswell Lee
  • Shyke A. Goldstein

Organizations

  • United States Naval Research Laboratory

Tags

DTIC Thesaurus Topics

  • Boundaries
  • Differential Equations
  • Equations
  • Mathematical Analysis
  • Mathematics
  • Partial Differential Equations

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)