Rosenbrock Type Methods for Solving Non-Linear Second-Order in Time Problems
In this work, we develop a new class of methods which have been created in order to numerically solve non-linear second-order in time problems in an efficient way. These methods are of the Rosenbrock type, and they can be seen as a generalization of these methods when they are applied to second-orde...
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| Tipo de documento: | artigo |
| Data de publicação: | 2021 |
| País: | España |
| Recursos: | Universidad Complutense de Madrid (UCM) |
| Repositório: | Docta Complutense |
| Idioma: | inglês |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/5016 |
| Acesso em linha: | https://hdl.handle.net/20.500.14352/5016 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Second-order in time problems Non-linear problems Rosenbrock type methods. Análisis Numérico 1206: Análisis Numérico |
| Resumo: | In this work, we develop a new class of methods which have been created in order to numerically solve non-linear second-order in time problems in an efficient way. These methods are of the Rosenbrock type, and they can be seen as a generalization of these methods when they are applied to second-order in time problems which have been previously transformed into first-order in time problems. As they also follow the ideas of Runge–Kutta–Nyström methods when solving second-order in time problems, we have called them Rosenbrock–Nyström methods. When solving non-linear problems, Rosenbrock–Nyström methods present less computational cost than implicit Runge–Kutta–Nyström ones, as the non-linear systems which arise at every intermediate stage when Runge–Kutta–Nyström methods are used are replaced with sequences of linear ones. |
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