Approximation of solutions of nonlinear initial-value problems by B-spline functions
Volume 92 / 2011
Banach Center Publications 92 (2011), 391-398 MSC: Primary 35F25; Secondary 41A15. DOI: 10.4064/bc92-0-27
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).