Szczegóły publikacji
Opis bibliograficzny
Adaptive mesh selection asymptotically guarantees a prescribed local error for systems of initial value problems / Bolesław KACEWICZ // Advances in Computational Mathematics ; ISSN 1019-7168. — 2018 — vol. 44 iss. 5, s. 1325–1344. — Bibliogr. s. 1344, Abstr. — Publikacja dostępna online od: 2017-12-26
Autor
Dane bibliometryczne
| ID BaDAP | 118165 |
|---|---|
| Data dodania do BaDAP | 2018-11-22 |
| Tekst źródłowy | URL |
| DOI | 10.1007/s10444-017-9584-2 |
| Rok publikacji | 2018 |
| Typ publikacji | artykuł w czasopiśmie |
| Otwarty dostęp |  |
| Czasopismo/seria | Advances in Computational Mathematics |
Abstract
We study potential advantages of adaptive mesh point selection for the solution of systems of initial value problems. For an optimal order discretization method, we propose an algorithm for successive selection of the mesh points, which only requires evaluations of the right-hand side function. The selection (asymptotically) guarantees that the maximum local error of the method does not exceed a prescribed level. The usage of the algorithm is not restricted to the chosen method; it can also be applied with any method from a general class. We provide a rigorous analysis of the cost of the proposed algorithm. It is shown that the cost is almost minimal, up to absolute constants, among all mesh selection algorithms. For illustration, we specify the advantage of the adaptive mesh over the uniform one. Efficiency of the adaptive algorithm results from automatic adjustment of the successive mesh points to the local behavior of the solution. Some numerical results illustrating theoretical findings are reported. © 2017, Springer Science+Business Media, LLC, part of Springer Nature.