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Journal of Applied Mathematics and Stochastic Analysis
Volume 5 (1992), Issue 1, Pages 69-82
http://dx.doi.org/10.1155/S1048953392000054

Numerical solutions of nonstandard first order initial value problems

Department of Mathematics, Sri Saihya Sat Institute of Higher Learning, Prasanthinilayam , Andhra Pradesh 515 134, India

Received 1 February 1990; Revised 1 February 1991

Copyright © 1992 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Differential equations of the form y=f(t,y,y), where f is not necessarily linear in its arguments, represent certain physical phenomena and are known for quite some time. The well known Clairut's and Chrystal's equations fall into this category. Earlier, we established the existence of a (unique) solution of the nonstandard initial value problem (NSTD IV P) y=f(t,y,y), y(t0)=y0 under certain natural hypotheses on f. In this paper we present some first order convergent numerical methods for finding the approximate solutions of the NST D I V Ps.