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

Numerical solutions of nonstandard first order initial value problems

M. Venkatesulu and P. D. N. Srinivasu

 Department of Mathematics, Sri Saihya Sat Institute of Higher Learning, Prasanthinilayam 515 134, Andhra Pradesh, India
Received 1 February 1990; Revised 1 February 1991

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.