An adaptive optimized Nyström method for second-order IVPs
Corresponding Author
Mufutau Ajani Rufai
Dipartimento di Matematica, Università Degli Studi di Bari Aldo Moro, Bari, 70125 Italy
Correspondence
Mufutau Ajani Rufai, Dipartimento di Matematica, Università Degli Studi di Bari Aldo Moro, Bari 70125, Italy.
Email: [email protected]
Communicated by: T. Monovasilis
Search for more papers by this authorFrancesca Mazzia
Dipartimento di Informatica, Università Degli Studi di Bari Aldo Moro, Bari, 70125 Italy
Search for more papers by this authorHiginio Ramos
Scientific Computing Group, Universidad de Salamanca, Plaza de la Merced, Salamanca, 37008 Spain
Escuela Politécnica Superior de Zamora, Campus Viriato, Zamora, 49022 Spain
Search for more papers by this authorCorresponding Author
Mufutau Ajani Rufai
Dipartimento di Matematica, Università Degli Studi di Bari Aldo Moro, Bari, 70125 Italy
Correspondence
Mufutau Ajani Rufai, Dipartimento di Matematica, Università Degli Studi di Bari Aldo Moro, Bari 70125, Italy.
Email: [email protected]
Communicated by: T. Monovasilis
Search for more papers by this authorFrancesca Mazzia
Dipartimento di Informatica, Università Degli Studi di Bari Aldo Moro, Bari, 70125 Italy
Search for more papers by this authorHiginio Ramos
Scientific Computing Group, Universidad de Salamanca, Plaza de la Merced, Salamanca, 37008 Spain
Escuela Politécnica Superior de Zamora, Campus Viriato, Zamora, 49022 Spain
Search for more papers by this authorAbstract
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.
CONFLICT OF INTEREST
This work does not have any conflict of interest.
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