A Tenth-Order Sixth-Derivative Block Method for Directly Solving Fifth-Order Initial Value Problems.
[EN]This work proposes a hybrid block numerical method of tenth order for the direct solution of fifth-order initial value problems. The formulas that constitute the block method are derived from a continuous approximation obtained through interpolation and collocation techniques. In order to obtain...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Universidad de Salamanca (USAL) |
| Repositorio: | GREDOS. Repositorio Institucional de la Universidad de Salamanca |
| OAI Identifier: | oai:gredos.usal.es:10366/156328 |
| Acceso en línea: | http://hdl.handle.net/10366/156328 |
| Access Level: | acceso abierto |
| Palabra clave: | Hybrid block method Fifth-order initial value problem Continuous approximation Interpolation Collocation linear stability 12 Matemáticas |
| Sumario: | [EN]This work proposes a hybrid block numerical method of tenth order for the direct solution of fifth-order initial value problems. The formulas that constitute the block method are derived from a continuous approximation obtained through interpolation and collocation techniques. In order to obtain better accuracy, sixth-order derivatives are incorporated to develop the formulas. The main characteristics of the method are analyzed, namely, the order, local truncation errors, zero-stability, consistency and convergence. The proposed strategy performs well, as shown by some numerical examples and the corresponding efficiency curves. Compared to existing numerical methods in the literature, the proposed method is competitive and the numerical approximations it provides are significantly close to the precise solutions. |
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