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...

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Detalles Bibliográficos
Autores: Ajani Rufai, Mufutau, Mazzia, Francesca, Ramos Calle, Higinio
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
Descripción
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.