Accession Number : AD0753915

Title :   The Method of Summary Representation.

Descriptive Note : Technical rept. Jul 66-Jun 67,

Corporate Author : NEW MEXICO UNIV ALBUQUERQUE

Personal Author(s) : Bradshaw,M. D.

Report Date : DEC 1972

Pagination or Media Count : 77

Abstract : The report describes a new mathematical technique for solving partial differential equations developed by G. N. Polozhii. The technique is illustrated by applying it to the solution of Laplace's equation in rectangular coordinates. The method of summary representation combines elements of commonly used analytical and finite difference techniques. Designed specifically for computer applications, the new technique is based upon the special properties of tridiagonal matrices. Use of the method of summary representation allows the general solution to be written down in a finite difference form especially suited for computation. Advantages of the new technique include the capability for calculating values at any selected point in the grid and provision for higher accuracy than conventional techniques. In addition, changes in the boundary conditions are very easily incorporated. Problems which can be described in rectangular geometry, including irregular shapes, are discussed. Specific numerical examples are given for four one-region situations and seven two-region situations. (Author)

Descriptors :   (*PARTIAL DIFFERENTIAL EQUATIONS, NUMERICAL ANALYSIS), DIFFERENCE EQUATIONS, INTEGRAL TRANSFORMS, CONFORMAL MAPPING, FOURIER ANALYSIS, APPROXIMATION(MATHEMATICS), MATRICES(MATHEMATICS), GEOMETRY, COMPUTER PROGRAMS, POTENTIAL THEORY, NUMERICAL INTEGRATION

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE