Accession Number : AD0895215
Title : Non-Iterative Numerical Solutions of Boundary-Value 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 difference-equation problem, which can be found under a large variety of circumstances. This analytical solution is used to set up and check a stepping-ahead process, during which the numerical solution of the boundary-value 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 non-homogeneous, 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 high-order 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