A new one-step method with three intermediate points in a variable step-size mode for stiff differential systems.

[EN]This work introduces a new one-step method with three intermediate points for solving stiff differential systems. These types of problems appear in different disciplines and, in particular, in problems derived from chemical reactions. In fact, the term “stiff”’ was coined by Curtiss and Hirschfe...

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Detalles Bibliográficos
Autores: Ramos Calle, Higinio, Rufai, Mufutau Ajani
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2022
País:España
Institución:Universidad de Salamanca (USAL)
Repositorio:GREDOS. Repositorio Institucional de la Universidad de Salamanca
OAI Identifier:oai:gredos.usal.es:10366/156338
Acceso en línea:http://hdl.handle.net/10366/156338
Access Level:acceso abierto
Palabra clave:Ordinary differential equations
Stiff problems
Variable step-size formulation
Error estimation and control
Collocation and interpolation techniques
12 Matemáticas
Descripción
Sumario:[EN]This work introduces a new one-step method with three intermediate points for solving stiff differential systems. These types of problems appear in different disciplines and, in particular, in problems derived from chemical reactions. In fact, the term “stiff”’ was coined by Curtiss and Hirschfelder in an article on problems of chemical kinetics (Hirschfelder, Proc Natl Acad Sci USA 38:235–243, 1952). The techniques of interpolation and collocation are used in the construction of the scheme. We consider a suitable polynomial to approximate the theoretical solution of the problem under consideration. The basic properties of the new scheme are analyzed. An embedded strategy is adopted to formulate the proposed scheme in a variable stepsize mode to get better performance. Finally, some models of initial-value problems, including ordinary and time-dependent partial differential equations, are solved numerically to assess the performance and efficiency of the proposed technique, with applications to real-world problems.