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Titel
Numerical integration of stiff problems using a new time-efficient hybrid block solver based on collocation and interpolation techniques.
Autor(es)
Schlagwort
L-stability
Order stars
Stiff problems
Efficiency curves
Clasificación UNESCO
12 Matemáticas
Fecha de publicación
2024
Verlag
Elsevier
Citación
Sania Qureshi, Higinio Ramos, Amanullah Soomro, Olusheye Aremu Akinfenwa, Moses Adebowale Akanbi, Numerical integration of stiff problems using a new time-efficient hybrid block solver based on collocation and interpolation techniques, Mathematics and Computers in Simulation, Volume 220, 2024, Pages 237-252, ISSN 0378-4754, https://doi.org/10.1016/j.matcom.2024.01.001. (https://www.sciencedirect.com/science/article/pii/S0378475424000016)
Resumen
[EN]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.
URI
ISSN
0378-4754
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