Structure-Preserving Algorithms for a Class of Dynamical Systems
Abstract In this paper, we study structure-preserving algorithms for dynamical systems defined by ordinary differential equations in Rn. The equations are assumed to be of the form ẏ = A(y)+D(y) +R(y), where A(y) is the conservative part subject to 〈A(y), y〉 = 0; D(y) is the damping part or the part...
Ausführliche Beschreibung
Autor*in: |
Wang, Ling-shu [verfasserIn] |
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Format: |
Artikel |
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Sprache: |
Englisch |
Erschienen: |
2007 |
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Anmerkung: |
© Springer-Verlag Berlin Heidelberg 2007 |
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Übergeordnetes Werk: |
Enthalten in: Acta mathematicae applicatae sinica / English series - Springer-Verlag, 2002, 23(2007), 1 vom: Jan., Seite 161-176 |
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Übergeordnetes Werk: |
volume:23 ; year:2007 ; number:1 ; month:01 ; pages:161-176 |
Links: |
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DOI / URN: |
10.1007/s10255-006-0361-0 |
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Katalog-ID: |
OLC2109953225 |
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10.1007/s10255-006-0361-0 doi (DE-627)OLC2109953225 (DE-He213)s10255-006-0361-0-p DE-627 ger DE-627 rakwb eng 510 VZ 31.80$jAngewandte Mathematik bkl Wang, Ling-shu verfasserin aut Structure-Preserving Algorithms for a Class of Dynamical Systems 2007 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2007 Abstract In this paper, we study structure-preserving algorithms for dynamical systems defined by ordinary differential equations in Rn. The equations are assumed to be of the form ẏ = A(y)+D(y) +R(y), where A(y) is the conservative part subject to 〈A(y), y〉 = 0; D(y) is the damping part or the part describing the coexistence of damping and expanding; R(y) reflects strange phenomenon of the system. It is shown that the numerical solutions generated by the symplectic Runge-Kutta(SRK) methods with bi > 0 ( i = 1, • • • , s) have long-time approximations to the exact ones, and these methods can describe the structural properties of the quadratic energy for these systems. Some numerical experiments and backward error analysis also show that these methods are better than other methods including the general algebraically stable Runge-Kutta(RK)methods. SRK methods numerical experiment backward error analysis Feng, Guang-hui aut Enthalten in Acta mathematicae applicatae sinica / English series Springer-Verlag, 2002 23(2007), 1 vom: Jan., Seite 161-176 (DE-627)363762353 (DE-600)2106495-7 (DE-576)105283274 0168-9673 nnns volume:23 year:2007 number:1 month:01 pages:161-176 https://doi.org/10.1007/s10255-006-0361-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT GBV_ILN_70 GBV_ILN_2018 GBV_ILN_2088 31.80$jAngewandte Mathematik VZ 106419005 (DE-625)106419005 AR 23 2007 1 01 161-176 |
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10.1007/s10255-006-0361-0 doi (DE-627)OLC2109953225 (DE-He213)s10255-006-0361-0-p DE-627 ger DE-627 rakwb eng 510 VZ 31.80$jAngewandte Mathematik bkl Wang, Ling-shu verfasserin aut Structure-Preserving Algorithms for a Class of Dynamical Systems 2007 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2007 Abstract In this paper, we study structure-preserving algorithms for dynamical systems defined by ordinary differential equations in Rn. The equations are assumed to be of the form ẏ = A(y)+D(y) +R(y), where A(y) is the conservative part subject to 〈A(y), y〉 = 0; D(y) is the damping part or the part describing the coexistence of damping and expanding; R(y) reflects strange phenomenon of the system. It is shown that the numerical solutions generated by the symplectic Runge-Kutta(SRK) methods with bi > 0 ( i = 1, • • • , s) have long-time approximations to the exact ones, and these methods can describe the structural properties of the quadratic energy for these systems. Some numerical experiments and backward error analysis also show that these methods are better than other methods including the general algebraically stable Runge-Kutta(RK)methods. SRK methods numerical experiment backward error analysis Feng, Guang-hui aut Enthalten in Acta mathematicae applicatae sinica / English series Springer-Verlag, 2002 23(2007), 1 vom: Jan., Seite 161-176 (DE-627)363762353 (DE-600)2106495-7 (DE-576)105283274 0168-9673 nnns volume:23 year:2007 number:1 month:01 pages:161-176 https://doi.org/10.1007/s10255-006-0361-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT GBV_ILN_70 GBV_ILN_2018 GBV_ILN_2088 31.80$jAngewandte Mathematik VZ 106419005 (DE-625)106419005 AR 23 2007 1 01 161-176 |
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10.1007/s10255-006-0361-0 doi (DE-627)OLC2109953225 (DE-He213)s10255-006-0361-0-p DE-627 ger DE-627 rakwb eng 510 VZ 31.80$jAngewandte Mathematik bkl Wang, Ling-shu verfasserin aut Structure-Preserving Algorithms for a Class of Dynamical Systems 2007 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2007 Abstract In this paper, we study structure-preserving algorithms for dynamical systems defined by ordinary differential equations in Rn. The equations are assumed to be of the form ẏ = A(y)+D(y) +R(y), where A(y) is the conservative part subject to 〈A(y), y〉 = 0; D(y) is the damping part or the part describing the coexistence of damping and expanding; R(y) reflects strange phenomenon of the system. It is shown that the numerical solutions generated by the symplectic Runge-Kutta(SRK) methods with bi > 0 ( i = 1, • • • , s) have long-time approximations to the exact ones, and these methods can describe the structural properties of the quadratic energy for these systems. Some numerical experiments and backward error analysis also show that these methods are better than other methods including the general algebraically stable Runge-Kutta(RK)methods. SRK methods numerical experiment backward error analysis Feng, Guang-hui aut Enthalten in Acta mathematicae applicatae sinica / English series Springer-Verlag, 2002 23(2007), 1 vom: Jan., Seite 161-176 (DE-627)363762353 (DE-600)2106495-7 (DE-576)105283274 0168-9673 nnns volume:23 year:2007 number:1 month:01 pages:161-176 https://doi.org/10.1007/s10255-006-0361-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT GBV_ILN_70 GBV_ILN_2018 GBV_ILN_2088 31.80$jAngewandte Mathematik VZ 106419005 (DE-625)106419005 AR 23 2007 1 01 161-176 |
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Abstract In this paper, we study structure-preserving algorithms for dynamical systems defined by ordinary differential equations in Rn. The equations are assumed to be of the form ẏ = A(y)+D(y) +R(y), where A(y) is the conservative part subject to 〈A(y), y〉 = 0; D(y) is the damping part or the part describing the coexistence of damping and expanding; R(y) reflects strange phenomenon of the system. It is shown that the numerical solutions generated by the symplectic Runge-Kutta(SRK) methods with bi > 0 ( i = 1, • • • , s) have long-time approximations to the exact ones, and these methods can describe the structural properties of the quadratic energy for these systems. Some numerical experiments and backward error analysis also show that these methods are better than other methods including the general algebraically stable Runge-Kutta(RK)methods. © Springer-Verlag Berlin Heidelberg 2007 |
abstractGer |
Abstract In this paper, we study structure-preserving algorithms for dynamical systems defined by ordinary differential equations in Rn. The equations are assumed to be of the form ẏ = A(y)+D(y) +R(y), where A(y) is the conservative part subject to 〈A(y), y〉 = 0; D(y) is the damping part or the part describing the coexistence of damping and expanding; R(y) reflects strange phenomenon of the system. It is shown that the numerical solutions generated by the symplectic Runge-Kutta(SRK) methods with bi > 0 ( i = 1, • • • , s) have long-time approximations to the exact ones, and these methods can describe the structural properties of the quadratic energy for these systems. Some numerical experiments and backward error analysis also show that these methods are better than other methods including the general algebraically stable Runge-Kutta(RK)methods. © Springer-Verlag Berlin Heidelberg 2007 |
abstract_unstemmed |
Abstract In this paper, we study structure-preserving algorithms for dynamical systems defined by ordinary differential equations in Rn. The equations are assumed to be of the form ẏ = A(y)+D(y) +R(y), where A(y) is the conservative part subject to 〈A(y), y〉 = 0; D(y) is the damping part or the part describing the coexistence of damping and expanding; R(y) reflects strange phenomenon of the system. It is shown that the numerical solutions generated by the symplectic Runge-Kutta(SRK) methods with bi > 0 ( i = 1, • • • , s) have long-time approximations to the exact ones, and these methods can describe the structural properties of the quadratic energy for these systems. Some numerical experiments and backward error analysis also show that these methods are better than other methods including the general algebraically stable Runge-Kutta(RK)methods. © Springer-Verlag Berlin Heidelberg 2007 |
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title_short |
Structure-Preserving Algorithms for a Class of Dynamical Systems |
url |
https://doi.org/10.1007/s10255-006-0361-0 |
remote_bool |
false |
author2 |
Feng, Guang-hui |
author2Str |
Feng, Guang-hui |
ppnlink |
363762353 |
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hochschulschrift_bool |
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doi_str |
10.1007/s10255-006-0361-0 |
up_date |
2024-07-04T04:27:41.351Z |
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1803621248635240448 |
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