Ibáñez González, JJ.; Hernández García, V.; Ruiz Martínez, PA.; Arias, E. (2011). A piecewise-linearized algorithm based on the Krylov subspace for solving stiff ODEs. Journal of Computational and Applied Mathematics. 235(7):1798-1804. https://doi.org/10.1016/j.cam.2010.07.012
Por favor, use este identificador para citar o enlazar este ítem: http://hdl.handle.net/10251/38361
Title:
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A piecewise-linearized algorithm based on the Krylov subspace for solving stiff ODEs
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Author:
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Ibáñez González, Jacinto Javier
Hernández García, Vicente
Ruiz Martínez, Pedro Antonio
Arias, Enrique
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UPV Unit:
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Universitat Politècnica de València. Departamento de Sistemas Informáticos y Computación - Departament de Sistemes Informàtics i Computació
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Issued date:
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Abstract:
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Numerical methods for solving Ordinary Differential Equations (ODEs) have received considerable attention in recent years. In this paper a piecewise-linearized algorithm based on Krylov subspaces for solving Initial Value ...[+]
Numerical methods for solving Ordinary Differential Equations (ODEs) have received considerable attention in recent years. In this paper a piecewise-linearized algorithm based on Krylov subspaces for solving Initial Value Problems (IVPs) is proposed. MATLAB versions for autonomous and non-autonomous ODEs of this algorithm have been implemented. These implementations have been compared with other piecewise-linearized algorithms based on Pad approximants, recently developed by the authors of this paper, comparing both precisions and computational costs in equal conditions. Four case studies have been used in the tests that come from stiff biology and chemical kinetics problems. Experimental results show the advantages of the proposed algorithms, especially when the dimension is increased in stiff problems. © 2009 Elsevier B.V. All rights reserved.
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Subjects:
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Initial Value Problem (IVP)
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Krylov subspace
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Linear Differential Equation (LDE)
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Ordinary Differential Equation (ODE)
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Pad approximants
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Piecewise-linearized methods
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Approximants
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Chemical kinetics
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Computational costs
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Linear differential equation
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Linearized algorithms
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Nonautonomous
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Piece-wise
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Stiff problem
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Algorithms
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Differentiation (calculus)
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Dynamical systems
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Initial value problems
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Linearization
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Numerical methods
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Ordinary differential equations
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Copyrigths:
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Reserva de todos los derechos
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Source:
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Journal of Computational and Applied Mathematics. (issn:
0377-0427
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DOI:
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10.1016/j.cam.2010.07.012
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Publisher:
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Elsevier
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Publisher version:
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http://dx.doi.org/10.1016/j.cam.2010.07.012
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Project ID:
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info:eu-repo/grantAgreement/MEC//CGL2007-66440-C04-03/ES/DESARROLLO DE UN MODELO REGIONAL DE CLIMA CON ACOPLAMIENTO ATMOSFERA-OCEANO Y LA OPTIMIZACION DEL CODIGO PARA SU EJECUCION EN CLUSTERS MASIVAMENTE PARALELOS./
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Thanks:
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This work was supported by the Spanish CICYT project CGL2007-66440-C04-03.
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Type:
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Artículo
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