DISCRETIZATION METHODS FOR RETARDED ORDINARY DIFFERENTIAL EQUATIONS.
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1964
- Accession Number
- AD0605362
Entities
People
- Mmmorley Alan Feldstein
Organizations
- University of California, Los Angeles