Bader, PKH.; Blanes Zamora, S.; Casas, F.; Ponsoda Miralles, E. (2016). Efficient numerical integration for N th-order non-autonomous linear differential equations. Journal of Computational and Applied Mathematics. 291:380-390. https://doi.org/10.1016/j.cam.2015.02.052
Por favor, use este identificador para citar o enlazar este ítem: http://hdl.handle.net/10251/81957
Title:
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Efficient numerical integration for N th-order non-autonomous linear differential equations
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Author:
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Bader, Philipp Karl Heinz
Blanes Zamora, Sergio
Casas, Fernando
Ponsoda Miralles, Enrique
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UPV Unit:
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Universitat Politècnica de València. Instituto Universitario de Matemática Multidisciplinar - Institut Universitari de Matemàtica Multidisciplinària
Universitat Politècnica de València. Escuela Técnica Superior de Ingenieros de Caminos, Canales y Puertos - Escola Tècnica Superior d'Enginyers de Camins, Canals i Ports
Universitat Politècnica de València. Escuela Técnica Superior de Ingeniería del Diseño - Escola Tècnica Superior d'Enginyeria del Disseny
Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada
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Issued date:
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Abstract:
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We consider the numerical integration of high-order linear non-homogeneous differential
equations, written as first order homogeneous linear equations, and using exponential
methods. Integrators like Magnus expansions ...[+]
We consider the numerical integration of high-order linear non-homogeneous differential
equations, written as first order homogeneous linear equations, and using exponential
methods. Integrators like Magnus expansions or commutator-free methods belong to the
class of exponential methods showing high accuracy on stiff or oscillatory problems, but
the computation of the exponentials or their action on vectors can be computationally
costly. The first order differential equations to be solved present a special algebraic
structure (associated with the companion matrix) which allows to build new methods
(hybrid methods between Magnus and commutator-free methods). The new methods are
of similar accuracy as standard exponential methods with a reduced complexity. Additional
parameters can be included into the scheme for optimization purposes. We illustrate how
these methods can be obtained and present several sixth-order methods which are tested
in several numerical experiments.
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Subjects:
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Higher order linear differential equation
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Nonautonomous coefficients
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Magnus expansion
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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.2015.02.052
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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.2015.02.052
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Project ID:
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info:eu-repo/grantAgreement/MINECO//MTM2013-46553-C3-3-P/ES/METODOS DE ESCISION Y COMPOSICION EN INTEGRACION NUMERICA GEOMETRICA. TEORIA Y APLICACIONES/
info:eu-repo/grantAgreement/UPV//PAID-06-11-2087/ES
info:eu-repo/grantAgreement/QNRF//#5-674-1-114/
info:eu-repo/grantAgreement/ME//AP2009-1892/ES/AP2009-1892/
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Thanks:
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PB, SB and FC acknowledge the Ministerio de Economia y Competitividad (Spain) for financial support through the coordinated project MTM2013-46553-C3-3-P. PB also acknowledges the support through the FPU fellowship AP2009-1892. ...[+]
PB, SB and FC acknowledge the Ministerio de Economia y Competitividad (Spain) for financial support through the coordinated project MTM2013-46553-C3-3-P. PB also acknowledges the support through the FPU fellowship AP2009-1892. FC has been additionally supported by NPRP GRANT #5-674-1-114 from the Qatar National Research Fund. EP has been partially supported by the Universitat Politecnica de Valencia under project 2087.
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Type:
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Artículo
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