
Accession Number : AD0751280
Title : Methods for the Global Solution of Differential Equations,
Corporate Author : MISSOURI UNIV KANSAS CITY DEPT OF MATHEMATICS
Personal Author(s) : Luke,Yudell L.
Report Date : 02 OCT 1972
Pagination or Media Count : 14
Abstract : In the paper, the author discusses a novel class of methods for obtaining global approximations to solutions of differential and other functional equations. Most of the techniques which have been devised for obtaining approximate solutions for differential equations are based on the following philosophy: one uses the equation as it stands, and then seeks to satisfy the equation approximately by various means such as power series, Fourier series, expansions in series of other functions or by use of finite difference schemes. Our approach reverses this procedure. The author solves an approximate equation, but solves it exactly. The methods discussed are thus philosophically more akin to the usual techniques for obtaining uniform asymptotic solutions of differential equations in the neighborhood of a turning point by constructing solutions of an equation which is similar to, but simpler than, the original equation. (Author)
Descriptors : (*DIFFERENTIAL EQUATIONS, APPROXIMATION(MATHEMATICS)), POLYNOMIALS, BOUNDARY VALUE PROBLEMS, MATRICES(MATHEMATICS), FOURIER ANALYSIS, SERIES(MATHEMATICS), NUMERICAL INTEGRATION, HYPERGEOMETRIC FUNCTIONS, BESSEL FUNCTIONS, NUMERICAL ANALYSIS
Subject Categories : Theoretical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE