Approximation of solutions of nonlinear initial-value problems by B-spline functions

• Autorzy: Krzysztof Wesołowski
• Języki publikacji: EN

Abstrakty

EN

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).

Kategorie tematyczne

• 35F25: Initial value problems for nonlinear first-order equations
• 41A15: Spline approximation

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2011
• Tom: 92
• Numer: 1
• Strony: 391-398

Daty

wydano

2011

Twórcy

autor

Krzysztof Wesołowski

• Department of Mathematics, Jagiellonian University, Łojasiewicza 6, 30-348 Kraków, Poland

Identyfikatory

DOI

10.4064/bc92-0-27