DISCRETIZATION METHODS FOR RETARDED ORDINARY DIFFERENTIAL EQUATIONS.
CALIFORNIA UNIV LOS ANGELES NUMERICAL ANALYSIS RESEARCH
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Let alphax be a continuous real function satisfying a alphax x b. Let ya y sub o, a given real number. Then the retarded ordinary differential equation yx fx, yx, yalphax has a unique local solution yx 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 yx, and shows that the discretization error is bounded. The bound, while a function of f, is independent of alpha. Author