Third derivative modification of k-step block Falkner methods for the numerical solution of second order initial-value problems

[EN]This paper is devoted to the development and analysis of a modified family of Falkner- type methods for solving differential systems of second-order initial-value problems. The approaches of collocation and interpolation are adopted to derive the new methods. These modified methods are implement...

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Detalles Bibliográficos
Autores: Ramos Calle, Higinio, Rufai, M.A.
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2018
País:España
Institución:Universidad de Salamanca (USAL)
Repositorio:GREDOS. Repositorio Institucional de la Universidad de Salamanca
OAI Identifier:oai:gredos.usal.es:10366/154412
Acceso en línea:http://hdl.handle.net/10366/154412
Access Level:acceso abierto
Palabra clave:Falkner-type methods
Second-order differential equations
Block methods
Stability analysis
12 Matemáticas
1299 Otras Especialidades Matemáticas. Matemáticas aplicadas
Descripción
Sumario:[EN]This paper is devoted to the development and analysis of a modified family of Falkner- type methods for solving differential systems of second-order initial-value problems. The approaches of collocation and interpolation are adopted to derive the new methods. These modified methods are implemented in block form to obtain the numerical solutions to the considered problems. The study of the properties of the proposed block Falkner-type methods reveals that they are consistent and zero-stable, and thus, convergent. From the stability analysis, it could be seen that the proposed Falkner methods have non-empty sta- bility regions for k = 2 , 3 , 4 . Some numerical test are presented to illustrate the efficiency of the proposed family.