Numerical integration of stiff problems using a new time-efficient hybrid block solver based on collocation and interpolation techniques.
[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...
| Autores: | , , , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2024 |
| País: | España |
| Institución: | Universidad de Salamanca (USAL) |
| Repositorio: | GREDOS. Repositorio Institucional de la Universidad de Salamanca |
| OAI Identifier: | oai:gredos.usal.es:10366/156088 |
| Acceso en línea: | http://hdl.handle.net/10366/156088 |
| Access Level: | acceso abierto |
| Palabra clave: | L-stability Order stars Stiff problems Efficiency curves 12 Matemáticas |
| Sumario: | [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. |
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