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Solving initial value problems for ordinary differential equations by two approaches: BDF and Piecewise-linearized methods

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Solving initial value problems for ordinary differential equations by two approaches: BDF and Piecewise-linearized methods

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dc.contributor.author Ibáñez González, Jacinto Javier es_ES
dc.contributor.author Hernández García, Vicente es_ES
dc.contributor.author Arias, E. es_ES
dc.contributor.author Ruiz Martínez, Pedro Antonio es_ES
dc.date.accessioned 2015-06-12T06:49:43Z
dc.date.available 2015-06-12T06:49:43Z
dc.date.issued 2009-05
dc.identifier.issn 0010-4655
dc.identifier.uri http://hdl.handle.net/10251/51582
dc.description.abstract Many scientific and engineering problems are described using Ordinary Differential Equations (ODEs), where the analytic solution is unknown. Much research has been done by the scientific community on developing numerical methods which can provide an approximate solution of the original ODE. In this work, two approaches have been considered based on BDF and Piecewise-linearized Methods. The approach based on BDF methods uses a Chord–Shamanskii iteration for computing the nonlinear system which is obtained when the BDF schema is used. Two approaches based on piecewise-linearized methods have also been considered. These approaches are based on a theorem proved in this paper which allows to compute the approximate solution at each time step by means of a block-oriented method based on diagonal Padé approximations. The difference between these implementations is in using or not using the scale and squaring technique. Five algorithms based on these approaches have been developed. MATLAB and Fortran versions of the above algorithms have been developed, comparing both precision and computational costs. BLAS and LAPACK libraries have been used in Fortran implementations. In order to compare in equality of conditions all implementations, algorithms with fixed step have been considered. Four of the five case studies analyzed come from biology and chemical kinetics stiff problems. Experimental results show the advantages of the proposed algorithms, especially when they are integrating stiff problems. es_ES
dc.language Inglés es_ES
dc.publisher Elsevier es_ES
dc.relation.ispartof Computer Physics Communications es_ES
dc.rights Reserva de todos los derechos es_ES
dc.subject Ordinary Differential Equation (ODE) es_ES
dc.subject Initial Value Problem (IVP) es_ES
dc.subject Backward Differentiation Formula (BDF) method es_ES
dc.subject Piecewise-linearized method es_ES
dc.subject Diagonal Padé approximation es_ES
dc.subject BLAS es_ES
dc.subject LAPACK es_ES
dc.subject.classification CIENCIAS DE LA COMPUTACION E INTELIGENCIA ARTIFICIAL es_ES
dc.subject.classification LENGUAJES Y SISTEMAS INFORMATICOS es_ES
dc.title Solving initial value problems for ordinary differential equations by two approaches: BDF and Piecewise-linearized methods es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1016/j.cpc.2008.11.013
dc.rights.accessRights Abierto es_ES
dc.contributor.affiliation Universitat Politècnica de València. Departamento de Sistemas Informáticos y Computación - Departament de Sistemes Informàtics i Computació es_ES
dc.description.bibliographicCitation Ibáñez González, JJ.; Hernández García, V.; Arias, E.; Ruíz Martínez, PA. (2009). Solving initial value problems for ordinary differential equations by two approaches: BDF and Piecewise-linearized methods. Computer Physics Communications. 180(5):712-723. doi:10.1016/j.cpc.2008.11.013 es_ES
dc.description.accrualMethod Senia es_ES
dc.relation.publisherversion http://dx.doi.org/10.1016/j.cpc.2008.11.013 es_ES
dc.description.upvformatpinicio 712 es_ES
dc.description.upvformatpfin 723 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 180 es_ES
dc.description.issue 5 es_ES
dc.relation.senia 35646


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