An adaptive optimized Nyström method for second‐order IVPs.
[EN]This research work deals with the development, analysis, and implementation of an adaptive optimized one-step Nyström method for solving second-order initial value problems of ODEs and time-dependent partial differential equations. The new method is developed through a collocation technique with...
| Autores: | , , |
|---|---|
| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2022 |
| País: | España |
| Institución: | Universidad de Salamanca (USAL) |
| Repositorio: | GREDOS. Repositorio Institucional de la Universidad de Salamanca |
| OAI Identifier: | oai:gredos.usal.es:10366/156313 |
| Acceso en línea: | http://hdl.handle.net/10366/156313 |
| Access Level: | acceso abierto |
| Palabra clave: | Collocation method Error estimation and control Ordinary and time-dependent partial differential equations Optimized Nyström method Variable step-size formulation 12 Matemáticas |
| Sumario: | [EN]This research work deals with the development, analysis, and implementation of an adaptive optimized one-step Nyström method for solving second-order initial value problems of ODEs and time-dependent partial differential equations. The new method is developed through a collocation technique with a new approach for selecting the collocation points. An embedding-like procedure is used to estimate the error of the proposed optimized method. The current approach has been used to compute efficiently approximate solutions to general second-order IVPs. The numerical experiments demonstrate that the introduced error estimation and step-size control strategy presented in this manuscript have produced a good performance compared to some of the other existing numerical methods. |
|---|