Time-efficient reformulation of the Lobatto III family of order eight.
[EN]Implicit block methods for solving initial value problems in ordinary differential equations are well-known among the contemporary scientific community, since they are cost-effective, self-starting, consistent, stable, and usually converge fast when applied to solve particularly stiff models. Th...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2022 |
| País: | España |
| Institución: | Universidad de Salamanca (USAL) |
| Repositorio: | GREDOS. Repositorio Institucional de la Universidad de Salamanca |
| OAI Identifier: | oai:gredos.usal.es:10366/156349 |
| Acceso en línea: | http://hdl.handle.net/10366/156349 |
| Access Level: | acceso abierto |
| Palabra clave: | Stiff systems ℋ-stability Local error Order stars Implicit stiff solver Efficiency curves Lobatto III Runge–Kutta methods 12 Matemáticas |
| Sumario: | [EN]Implicit block methods for solving initial value problems in ordinary differential equations are well-known among the contemporary scientific community, since they are cost-effective, self-starting, consistent, stable, and usually converge fast when applied to solve particularly stiff models. These characteristics of block methods are the primary reasons for the one-step optimized block method devised in the present research study with three off-grid points. Theoretical analysis, including the order of convergence, consistency, zero-stability, A-stability, order stars, and the local truncation error, are considered. The obtained method may be categorized as the well-known Lobatto IIIA Runge–Kutta method. The superiority of the devised method over various existing approaches having similar features is proved via numerical simulations of stiff and nonlinear differential systems. Furthermore, a suitable reformulation of the devised method results in considerable savings in computation time, as revealed through the efficiency plots. This turns out in a strategy to reformulate Runge–Kutta type methods in order to get a better performance. |
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