This note is motivated by [GGG], where an algorithm finding functions close to solutions of a given initial value-problem has been proposed (this algorithm has been recalled in Theorem 2.2). In this paper we present a commonly used definition and basic facts concerning B-spline functions and use them to improve the mentioned algorithm. This leads us to a better estimate of the Cauchy problem solution under some additional assumption on f appearing in the Cauchy problem. We also estimate the accuracy of the method (Theorem 2.6).
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc92-0-27,
author = {Krzysztof Weso\l owski},
title = {Approximation of solutions of nonlinear initial-value problems by B-spline functions},
journal = {Banach Center Publications},
volume = {95},
year = {2011},
pages = {391-398},
zbl = {05980567},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc92-0-27}
}
Krzysztof Wesołowski. Approximation of solutions of nonlinear initial-value problems by B-spline functions. Banach Center Publications, Tome 95 (2011) pp. 391-398. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc92-0-27/