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An adaptive optimized Runge-Kutta-Nyström method for second-order IVPs
  • Mufutau Ajani Rufai,
  • Francesca Mazzia,
Mufutau Ajani Rufai
University of Bari Aldo Moro Department of Informatics

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Francesca Mazzia
University of Bari Aldo Moro Department of Informatics
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University of Salamanca
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This research paper is concerned with developing, analyzing, and implementing an adaptive optimized one-step block Nyström method for solving second-order initial value problems of ODEs and time-dependent partial differential equations. The new technique is developed through a collocation method 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 produced approximate solutions to real-world oscillatory, periodic and stiff application problems. The numerical experiments demonstrate that the introduced error estimation and stepsize control strategy presented in this manuscript has produced a good performance compared with some of the other existing numerical methods.
08 Feb 2022Submitted to Mathematical Methods in the Applied Sciences
09 Feb 2022Submission Checks Completed
09 Feb 2022Assigned to Editor
20 Feb 2022Reviewer(s) Assigned
15 Jun 2022Review(s) Completed, Editorial Evaluation Pending
08 Jul 2022Editorial Decision: Revise Major
03 Oct 20221st Revision Received
05 Oct 2022Submission Checks Completed
05 Oct 2022Assigned to Editor
06 Oct 2022Reviewer(s) Assigned
07 Oct 2022Review(s) Completed, Editorial Evaluation Pending
09 Dec 2022Editorial Decision: Accept