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