
Accession Number : AD0895215
Title : NonIterative Numerical Solutions of BoundaryValue Problems,
Corporate Author : NAVAL ORDNANCE LAB WHITE OAK MD
Personal Author(s) : Hyman, Morton A.
Report Date : 22 OCT 1951
Pagination or Media Count : 44
Abstract : Use is made of the exact anlaytical solution of a related differenceequation problem, which can be found under a large variety of circumstances. This analytical solution is used to set up and check a steppingahead process, during which the numerical solution of the boundaryvalue problem is obtained as though the governing differential equation were hyperbolic instead of elliptic. This paper discusses application of the technique when the governing equation is linear; this equation may be nonhomogeneous, of any order, and with any number of independent variables; moreover, the region over which the equation is solved can be geometrically irregular. Furthermore, since the technique in effect solves a highorder system of simultaneous linear equations (of simple but nontrivial structure), it constitutes a new approach to matrix inversion.
Descriptors : (*BOUNDARY VALUE PROBLEMS, NUMERICAL ANALYSIS), DIFFERENCE EQUATIONS, SERIES(MATHEMATICS), BOUNDARY VALUE PROBLEMS, MATRICES(MATHEMATICS).
Subject Categories : Theoretical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE