ON THE NUMERICAL SOLUTION OF BOUNDARY-VALUE PROBLEMS FOR ELLIPTIC DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS.

Abstract

Let g sub k (k = 0,...,m) be rectangles with sides parallel to the coordinate axes in R sub 2 and assume that the g sub k (k = 1,...,m) all intersect g sub o. Let G = (U sub k, superscript m) = (O superscript g)k and consider the Dirichlet problem in G for the equation delta u - lambda u = f, lambda = or > 0. The problem is discretized by means of the ordinary five-point formula, and the resulting finite linear system of equations is solved by an iterative scheme, which is a finite-difference analog of the Schwartz alternating procedure from potential theory, using the fact that for a single rectangle the solution admits an explicit representation in the form of a finite sum. (Author)

Document Details

Document Type
Technical Report
Publication Date
Aug 15, 1969
Accession Number
AD0693366

Entities

People

  • I. M. Lyashenko
  • V. I. Didenko

Organizations

  • Johns Hopkins University Applied Physics Laboratory

Tags

DTIC Thesaurus Topics

  • Boundaries
  • Boundary Value Problems
  • Coefficients
  • Differential Equations
  • Equations
  • Linear Systems
  • Mathematical Analysis
  • Mathematics
  • Potential Theory

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Graph Algorithms and Convex Optimization.