 Numerical integration of stiff problems using a new time-efficient hybrid block solver based on collocation and interpolation techniquesSania Qureshi, Higinio Ramos, Amanullah Soomro, Olusheye Aremu Akinfenwa and Moses Adebowale Akanbi Mathematics and Computers in Simulation (MATCOM), 2024, vol. 220, issue C, 237-252 Abstract: In this study, an optimal L-stable time-efficient hybrid block method with a relative measure of stability is developed for solving stiff systems in ordinary differential equations. The derivation resorts to interpolation and collocation techniques over a single step with two intermediate points, resulting in an efficient one-step method. The optimization of the two off-grid points is achieved by means of the local truncation error (LTE) of the main formula. The theoretical analysis shows that the method is consistent, zero-stable, seventh-order convergent for the main formula, and L-stable. The highly stiff systems solved with the proposed and other algorithms (even of higher-order than the proposed one) proved the efficiency of the former in the context of several types of errors, precision factors, and computational time. Keywords: ℒ-stability; Order stars; Stiff problems; Efficiency curves (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:220:y:2024:i:c:p:237-252 DOI: 10.1016/j.matcom.2024.01.001 Access Statistics for this article Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier |
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