Numerical solution of boundary value problems by using an optimized two-step block method.
[EN]This paper aims at the application of an optimized two-step hybrid block method for solving boundary value problems with different types of boundary conditions. The proposed approach produces simultaneously approximations at all the grid points after solving an algebraic system of equations. 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:10366/157032 |
| Acceso en línea: | http://hdl.handle.net/10366/157032 |
| Access Level: | acceso abierto |
| Palabra clave: | Ordinary differential equations Boundary value problems Optimized hybrid block method Homotopy-type strategy Convergence analysis 12 Matemáticas |
| Sumario: | [EN]This paper aims at the application of an optimized two-step hybrid block method for solving boundary value problems with different types of boundary conditions. The proposed approach produces simultaneously approximations at all the grid points after solving an algebraic system of equations. The final approximate solution is obtained through a homotopy-type strategy which is used in order to get starting values for Newton’s method. The convergence analysis shows that the proposed method has at least fifth order of convergence. Some numerical experiments such as Bratu’s problem, singularly perturbed, and nonlinear system of BVPs are presented to illustrate the better performance of the proposed approach in comparison with other methods available in the recent literature. |
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