Accession Number : AD0605362

Title :   DISCRETIZATION METHODS FOR RETARDED ORDINARY DIFFERENTIAL EQUATIONS.

Descriptive Note : Doctoral tthesis,

Corporate Author : CALIFORNIA UNIV LOS ANGELES NUMERICAL ANALYSIS RESEARCH

Personal Author(s) : Feldstein,MMMorley Alan

Report Date : AUG 1964

Pagination or Media Count : 64

Abstract : Let alpha(x) be a continuous real function satisfying a < alpha(x) < x < b. Let y(a) = y sub o, a given real number. Then the retarded ordinary differential equation y'(x) = f(x, y(x), y(alpha(x)) has a unique local solution y(x) provided that f is continuous in its first argument and satisfies a Lip sub 1 condition in its other arguments. The purpose of this paper is to investigate constructive methods for solving this initial value problem. The discrete variable approach is used. Chapter 1 introduces a first order one step algorithm, shows that under suitable hypotheses it converges uniformly on finite intervals to the unique solution y(x), and shows that the discretization error is bounded. (The bound, while a function of f, is independent of alpha.) (Author)

Descriptors :   (*DIFFERENTIAL EQUATIONS, NUMERICAL ANALYSIS), (*NUMERICAL ANALYSIS, DIFFERENTIAL EQUATIONS), THEOREMS, INEQUALITIES, SERIES(MATHEMATICS), PERTURBATION THEORY, SEQUENCES(MATHEMATICS), INTEGRALS, BOUNDARY VALUE PROBLEMS, NUMERICAL METHODS AND PROCEDURES

Distribution Statement : APPROVED FOR PUBLIC RELEASE