Accession Number : AD0693366

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

Descriptive Note : APL Library bulletin translations series,

Corporate Author : JOHNS HOPKINS UNIV SILVER SPRING MD APPLIED PHYSICS LAB

Personal Author(s) : Didenko,V. I. ; Lyashenko,I. M.

Report Date : 15 AUG 1969

Pagination or Media Count : 17

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)

Descriptors :   (*PARTIAL DIFFERENTIAL EQUATIONS, *BOUNDARY VALUE PROBLEMS), (*NUMERICAL INTEGRATION, *NUMERICAL ANALYSIS), DIFFERENCE EQUATIONS, MATRICES(MATHEMATICS), ITERATIONS, POTENTIAL THEORY, TOPOLOGY, THEOREMS, USSR

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE