Numerical solutions of nonstandard first order initial value problems
type: Item
instance of: scholarly article
title: Numerical solutions of nonstandard first order initial value problems
zbMATH Open document ID: 0762.65045
DOI: 10.1155/S1048953392000054
author: M. Venkatesulu
author: Pichika D. N. Srinivasu
published in: Journal of Applied Mathematics and Stochastic Analysis
publication date: 1992-06-28T00:00:00Z
full work available at URL: https://eudml.org/doc/46798
review text: The nonstandard initial value problem (*) \(y'(t)=f(t,y(t),y'(t))\), \(y(t_ 0)=y_ 0\) is considered. Under some assumptions on the function \(f\) the existence and uniqueness of the right hand side local solution of the problem (*) is proved. Four numerical schemes linearly convergent to the solution of the problem (*) are presented. For all schemes convergence and error estimates are discussed. A numerical example for various stepsizes is solved using these schemes. The graphs of solutions are presented.
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 36755
zbMATH Keywords: linear convergence
zbMATH Keywords: nonstandard initial value problem
zbMATH Keywords: local solution
zbMATH Keywords: error estimate
zbMATH Keywords: numerical example
reviewed by: Józef Kalinowski
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 36755