Numerical solutions of nonstandard first order initial value problems. (1992)

• Record Type: Journal Article
• Authors: Venkatesulu, M.; Srinivasu, P. D. N.
• Is Part Of: Journal of applied mathematics and stochastic analysis. Volume 5:Number 1(1992)
• Page Start: 69
• Page End: 82
• Publication Date: 1992
• Subjects: nonstandard initial value problem -- existence -- unique solution -- real valued -- continuous -- differentiable -- numerical scheme -- inequality -- partition -- approximate -- algorithm -- influence -- round-off error -- estimate -- truncation; Mathematical models -- Periodicals; Computer simulation -- Periodicals; Computer science -- Mathematics -- Periodicals; Computer science -- Mathematics; Computer simulation; Mathematical models; Applied Mathematics; Periodicals; Electronic journals; 519.22
• DOI: 10.1155/S1048953392000054
• Languages: English
• ISSNs: 1048-9533

Abstract

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 ( t 0 ) = y 0 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.