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...

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Detalles Bibliográficos
Autores: Ramos Calle, Higinio, Momoh, Adelegan Lukuman
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
Descripción
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.