Finite Difference Methods for Polar Coordinate Systems.

Abstract

This document discusses finite difference methods for partial differential equations on polar and spherical coordinate systems. The distinctive feature of these coordinate systems is the coordinate system singularity at the origin. The authors show how to accurately and conveniently determine the solution at the origin for both scalar and vector fields. They also discuss the Fourier method to approximate derivatives with respect to the angular variable in polar coordinates. Computational examples are presented illustrating the accuracy and efficiency of the method for hyperbolic and elliptic equations, and also for the computation of vector fields at the origin. Keywords: guide(coordinate); quadrative formulas.

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Document Details

Document Type
Technical Report
Publication Date
Apr 01, 1986
Accession Number
ADA167512

Entities

People

  • John C. Strikwerda
  • Yvonne Nagel

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Accuracy
  • Boundary Value Problems
  • Computations
  • Coordinate Systems
  • Difference Equations
  • Differential Equations
  • Equations
  • Grids
  • Integrals
  • Iterations
  • Mathematics
  • Military Research
  • Numerical Analysis
  • Periodic Functions
  • Poisson Equation
  • United States
  • Wave Equations

Readers

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