Efficient numerical integration of NNth-order non-autonomous linear differential equations
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Otros documentos de la autoría: Bader, Philipp; Blanes, Sergio; Casas, Fernando; Ponsoda, Enrique
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Mostrar el registro completo del ítemcomunitat-uji-handle:10234/9
comunitat-uji-handle2:10234/7037
comunitat-uji-handle3:10234/8635
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http://dx.doi.org/10.1016/j.cam.2015.02.052 |
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Título
Efficient numerical integration of NNth-order non-autonomous linear differential equationsFecha de publicación
2016Editor
ElsevierISSN
0377-0427Cita bibliográfica
BADER, Philipp, et al. Efficient numerical integration of Nth-order non-autonomous linear differential equations. Journal of Computational and Applied Mathematics, 2016, vol. 291, p. 380-390.Tipo de documento
info:eu-repo/semantics/articleVersión de la editorial
http://www.sciencedirect.com/science/article/pii/S0377042715001399Versión
info:eu-repo/semantics/publishedVersionPalabras clave / Materias
Resumen
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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Journal of Computational and Applied Mathematics, 2016, vol. 291Derechos de acceso
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