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