General relaxation methods for initial-value problems with application to multistep schemes
| Autor: | David I. Ketcheson, Lajos Lóczi, Hendrik Ranocha |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
65L06
65L20 65M12 65M70 65P10 37M99 Applied Mathematics Numerical analysis Relaxation (iterative method) Context (language use) Numerical Analysis (math.NA) 010103 numerical & computational mathematics 01 natural sciences 010101 applied mathematics Computational Mathematics General linear methods FOS: Mathematics Dissipative system Initial value problem Applied mathematics Order (group theory) Mathematics - Numerical Analysis 0101 mathematics Mathematics |
| Zdroj: | Numerische Mathematik. 146:875-906 |
| ISSN: | 0945-3245 0029-599X |
| DOI: | 10.1007/s00211-020-01158-4 |
| Popis: | Recently, an approach known as relaxation has been developed for preserving the correct evolution of a functional in the numerical solution of initial-value problems, using Runge-Kutta methods. We generalize this approach to multistep methods, including all general linear methods of order two or higher, and many other classes of schemes. We prove the existence of a valid relaxation parameter and high-order accuracy of the resulting method, in the context of general equations, including but not limited to conservative or dissipative systems. The theory is illustrated with several numerical examples. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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