A NUMERICAL INVESTIGATION AND UTILIZATION OF GREEN'S FUNCTIONS.

Abstract

The Green's functions for the Laplacian operator and the modified Helmholtz equation were obtained numerically, for a two-dimensional square, using a finite difference approach. The discrete Green's functions were then employed to obtain numerical solutions, in summation form, for the Laplace's, Poisson's, and diffusion equations for a square, subject to Dirichlet boundary conditions. Comparative studies with analytical methods showed the numerical determination of the Green's functions to be a rapid and accurate method. When used to solve the above mentioned equations, the summation process proved to be as accurate and, in some cases, more rapid than the fastest iterative techniques. (Author)

Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1968
Accession Number
AD0835168

Entities

People

  • Sanford Gallof

Organizations

  • Air Force Institute of Technology

Tags

DTIC Thesaurus Topics

  • Boundaries
  • Differential Equations
  • Diffusion
  • Equations
  • Helmholtz Equations
  • Mathematics
  • Partial Differential Equations
  • Two Dimensional

Readers

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