An Optimized Two-Step Hybrid Block Method Formulated in Variable Step-Size Mode for Integrating $y''=f(x,y,y')$ Numerically.
[EN]An optimized two-step hybrid block method is presented for integrating general second order initial value problems numerically. The method considers two intra-step points which are selected adequately in order to optimize the local truncation errors of the main formulas for the solution and the...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2019 |
| País: | España |
| Institución: | Universidad de Salamanca (USAL) |
| Repositorio: | GREDOS. Repositorio Institucional de la Universidad de Salamanca |
| OAI Identifier: | oai:gredos.usal.es:10366/157094 |
| Acceso en línea: | http://hdl.handle.net/10366/157094 |
| Access Level: | acceso abierto |
| Palabra clave: | Ordinary differential equations Second-order initial value problems Hybrid block method Optimization strategy Variable step-size 12 Matemáticas |
| Sumario: | [EN]An optimized two-step hybrid block method is presented for integrating general second order initial value problems numerically. The method considers two intra-step points which are selected adequately in order to optimize the local truncation errors of the main formulas for the solution and the first derivative at the final point of the block. The new proposed method is consistent, zero-stable and has seventh algebraic order of convergence. To illustrate the performance of the method, some numerical experiments are presented for solving this kind of problems, in comparison with methods of similar characteristics in the literature. |
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