Asymptotic stability analysis of Runge–Kutta methods for differential-algebraic equations with multiple delays
Abstract This paper deals with asymptotic stability of differential-algebraic equations with multiple delays and numerical solutions generated by Runge–Kutta methods combined with Lagrange interpolation. We study the solvability and asymptotic stability of delay differential-algebraic equations and...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Wu, Meijun [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2021 |
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| Schlagwörter: |
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| Anmerkung: |
© Istituto di Informatica e Telematica (IIT) 2021 |
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| Übergeordnetes Werk: |
Enthalten in: Calcolo - Springer International Publishing, 1964, 58(2021), 3 vom: 22. Juli |
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| Übergeordnetes Werk: |
volume:58 ; year:2021 ; number:3 ; day:22 ; month:07 |
| Links: |
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| DOI / URN: |
10.1007/s10092-021-00428-3 |
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OLC2126783057 |
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| 520 | |a Abstract This paper deals with asymptotic stability of differential-algebraic equations with multiple delays and numerical solutions generated by Runge–Kutta methods combined with Lagrange interpolation. We study the solvability and asymptotic stability of delay differential-algebraic equations and present some sufficient conditions for the zero solution to be asymptotically stable. A sufficient and necessary condition for the asymptotic stability of Runge–Kutta methods is provided. Further, some results on the asymptotic stability of high order Runge–Kutta methods are presented. Finally, two numerical examples are given to illustrate the numerical stability of the Runge–Kutta methods. | ||
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10.1007/s10092-021-00428-3 doi (DE-627)OLC2126783057 (DE-He213)s10092-021-00428-3-p DE-627 ger DE-627 rakwb eng 510 VZ Wu, Meijun verfasserin aut Asymptotic stability analysis of Runge–Kutta methods for differential-algebraic equations with multiple delays 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Istituto di Informatica e Telematica (IIT) 2021 Abstract This paper deals with asymptotic stability of differential-algebraic equations with multiple delays and numerical solutions generated by Runge–Kutta methods combined with Lagrange interpolation. We study the solvability and asymptotic stability of delay differential-algebraic equations and present some sufficient conditions for the zero solution to be asymptotically stable. A sufficient and necessary condition for the asymptotic stability of Runge–Kutta methods is provided. Further, some results on the asymptotic stability of high order Runge–Kutta methods are presented. Finally, two numerical examples are given to illustrate the numerical stability of the Runge–Kutta methods. Asymptotic stability Delay differential-algebraic equation Runge–Kutta method Numerical asymptotic stability Yu, Quanhong aut Kuang, Jiaoxun aut Tian, Hongjiong aut Enthalten in Calcolo Springer International Publishing, 1964 58(2021), 3 vom: 22. Juli (DE-627)129456330 (DE-600)199549-2 (DE-576)014819511 0008-0624 nnns volume:58 year:2021 number:3 day:22 month:07 https://doi.org/10.1007/s10092-021-00428-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_90 AR 58 2021 3 22 07 |
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10.1007/s10092-021-00428-3 doi (DE-627)OLC2126783057 (DE-He213)s10092-021-00428-3-p DE-627 ger DE-627 rakwb eng 510 VZ Wu, Meijun verfasserin aut Asymptotic stability analysis of Runge–Kutta methods for differential-algebraic equations with multiple delays 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Istituto di Informatica e Telematica (IIT) 2021 Abstract This paper deals with asymptotic stability of differential-algebraic equations with multiple delays and numerical solutions generated by Runge–Kutta methods combined with Lagrange interpolation. We study the solvability and asymptotic stability of delay differential-algebraic equations and present some sufficient conditions for the zero solution to be asymptotically stable. A sufficient and necessary condition for the asymptotic stability of Runge–Kutta methods is provided. Further, some results on the asymptotic stability of high order Runge–Kutta methods are presented. Finally, two numerical examples are given to illustrate the numerical stability of the Runge–Kutta methods. Asymptotic stability Delay differential-algebraic equation Runge–Kutta method Numerical asymptotic stability Yu, Quanhong aut Kuang, Jiaoxun aut Tian, Hongjiong aut Enthalten in Calcolo Springer International Publishing, 1964 58(2021), 3 vom: 22. Juli (DE-627)129456330 (DE-600)199549-2 (DE-576)014819511 0008-0624 nnns volume:58 year:2021 number:3 day:22 month:07 https://doi.org/10.1007/s10092-021-00428-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_90 AR 58 2021 3 22 07 |
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10.1007/s10092-021-00428-3 doi (DE-627)OLC2126783057 (DE-He213)s10092-021-00428-3-p DE-627 ger DE-627 rakwb eng 510 VZ Wu, Meijun verfasserin aut Asymptotic stability analysis of Runge–Kutta methods for differential-algebraic equations with multiple delays 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Istituto di Informatica e Telematica (IIT) 2021 Abstract This paper deals with asymptotic stability of differential-algebraic equations with multiple delays and numerical solutions generated by Runge–Kutta methods combined with Lagrange interpolation. We study the solvability and asymptotic stability of delay differential-algebraic equations and present some sufficient conditions for the zero solution to be asymptotically stable. A sufficient and necessary condition for the asymptotic stability of Runge–Kutta methods is provided. Further, some results on the asymptotic stability of high order Runge–Kutta methods are presented. Finally, two numerical examples are given to illustrate the numerical stability of the Runge–Kutta methods. Asymptotic stability Delay differential-algebraic equation Runge–Kutta method Numerical asymptotic stability Yu, Quanhong aut Kuang, Jiaoxun aut Tian, Hongjiong aut Enthalten in Calcolo Springer International Publishing, 1964 58(2021), 3 vom: 22. Juli (DE-627)129456330 (DE-600)199549-2 (DE-576)014819511 0008-0624 nnns volume:58 year:2021 number:3 day:22 month:07 https://doi.org/10.1007/s10092-021-00428-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_90 AR 58 2021 3 22 07 |
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10.1007/s10092-021-00428-3 doi (DE-627)OLC2126783057 (DE-He213)s10092-021-00428-3-p DE-627 ger DE-627 rakwb eng 510 VZ Wu, Meijun verfasserin aut Asymptotic stability analysis of Runge–Kutta methods for differential-algebraic equations with multiple delays 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Istituto di Informatica e Telematica (IIT) 2021 Abstract This paper deals with asymptotic stability of differential-algebraic equations with multiple delays and numerical solutions generated by Runge–Kutta methods combined with Lagrange interpolation. We study the solvability and asymptotic stability of delay differential-algebraic equations and present some sufficient conditions for the zero solution to be asymptotically stable. A sufficient and necessary condition for the asymptotic stability of Runge–Kutta methods is provided. Further, some results on the asymptotic stability of high order Runge–Kutta methods are presented. Finally, two numerical examples are given to illustrate the numerical stability of the Runge–Kutta methods. Asymptotic stability Delay differential-algebraic equation Runge–Kutta method Numerical asymptotic stability Yu, Quanhong aut Kuang, Jiaoxun aut Tian, Hongjiong aut Enthalten in Calcolo Springer International Publishing, 1964 58(2021), 3 vom: 22. Juli (DE-627)129456330 (DE-600)199549-2 (DE-576)014819511 0008-0624 nnns volume:58 year:2021 number:3 day:22 month:07 https://doi.org/10.1007/s10092-021-00428-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_90 AR 58 2021 3 22 07 |
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10.1007/s10092-021-00428-3 doi (DE-627)OLC2126783057 (DE-He213)s10092-021-00428-3-p DE-627 ger DE-627 rakwb eng 510 VZ Wu, Meijun verfasserin aut Asymptotic stability analysis of Runge–Kutta methods for differential-algebraic equations with multiple delays 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Istituto di Informatica e Telematica (IIT) 2021 Abstract This paper deals with asymptotic stability of differential-algebraic equations with multiple delays and numerical solutions generated by Runge–Kutta methods combined with Lagrange interpolation. We study the solvability and asymptotic stability of delay differential-algebraic equations and present some sufficient conditions for the zero solution to be asymptotically stable. A sufficient and necessary condition for the asymptotic stability of Runge–Kutta methods is provided. Further, some results on the asymptotic stability of high order Runge–Kutta methods are presented. Finally, two numerical examples are given to illustrate the numerical stability of the Runge–Kutta methods. Asymptotic stability Delay differential-algebraic equation Runge–Kutta method Numerical asymptotic stability Yu, Quanhong aut Kuang, Jiaoxun aut Tian, Hongjiong aut Enthalten in Calcolo Springer International Publishing, 1964 58(2021), 3 vom: 22. Juli (DE-627)129456330 (DE-600)199549-2 (DE-576)014819511 0008-0624 nnns volume:58 year:2021 number:3 day:22 month:07 https://doi.org/10.1007/s10092-021-00428-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_90 AR 58 2021 3 22 07 |
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Asymptotic stability analysis of Runge–Kutta methods for differential-algebraic equations with multiple delays |
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Abstract This paper deals with asymptotic stability of differential-algebraic equations with multiple delays and numerical solutions generated by Runge–Kutta methods combined with Lagrange interpolation. We study the solvability and asymptotic stability of delay differential-algebraic equations and present some sufficient conditions for the zero solution to be asymptotically stable. A sufficient and necessary condition for the asymptotic stability of Runge–Kutta methods is provided. Further, some results on the asymptotic stability of high order Runge–Kutta methods are presented. Finally, two numerical examples are given to illustrate the numerical stability of the Runge–Kutta methods. © Istituto di Informatica e Telematica (IIT) 2021 |
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Abstract This paper deals with asymptotic stability of differential-algebraic equations with multiple delays and numerical solutions generated by Runge–Kutta methods combined with Lagrange interpolation. We study the solvability and asymptotic stability of delay differential-algebraic equations and present some sufficient conditions for the zero solution to be asymptotically stable. A sufficient and necessary condition for the asymptotic stability of Runge–Kutta methods is provided. Further, some results on the asymptotic stability of high order Runge–Kutta methods are presented. Finally, two numerical examples are given to illustrate the numerical stability of the Runge–Kutta methods. © Istituto di Informatica e Telematica (IIT) 2021 |
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Abstract This paper deals with asymptotic stability of differential-algebraic equations with multiple delays and numerical solutions generated by Runge–Kutta methods combined with Lagrange interpolation. We study the solvability and asymptotic stability of delay differential-algebraic equations and present some sufficient conditions for the zero solution to be asymptotically stable. A sufficient and necessary condition for the asymptotic stability of Runge–Kutta methods is provided. Further, some results on the asymptotic stability of high order Runge–Kutta methods are presented. Finally, two numerical examples are given to illustrate the numerical stability of the Runge–Kutta methods. © Istituto di Informatica e Telematica (IIT) 2021 |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000naa a22002652 4500</leader><controlfield tag="001">OLC2126783057</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230505132625.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">230505s2021 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s10092-021-00428-3</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2126783057</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)s10092-021-00428-3-p</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Wu, Meijun</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Asymptotic stability analysis of Runge–Kutta methods for differential-algebraic equations with multiple delays</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2021</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Istituto di Informatica e Telematica (IIT) 2021</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract This paper deals with asymptotic stability of differential-algebraic equations with multiple delays and numerical solutions generated by Runge–Kutta methods combined with Lagrange interpolation. We study the solvability and asymptotic stability of delay differential-algebraic equations and present some sufficient conditions for the zero solution to be asymptotically stable. A sufficient and necessary condition for the asymptotic stability of Runge–Kutta methods is provided. Further, some results on the asymptotic stability of high order Runge–Kutta methods are presented. Finally, two numerical examples are given to illustrate the numerical stability of the Runge–Kutta methods.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Asymptotic stability</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Delay differential-algebraic equation</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Runge–Kutta method</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Numerical asymptotic stability</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Yu, Quanhong</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Kuang, Jiaoxun</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Tian, Hongjiong</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Calcolo</subfield><subfield code="d">Springer International Publishing, 1964</subfield><subfield code="g">58(2021), 3 vom: 22. Juli</subfield><subfield code="w">(DE-627)129456330</subfield><subfield code="w">(DE-600)199549-2</subfield><subfield code="w">(DE-576)014819511</subfield><subfield code="x">0008-0624</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:58</subfield><subfield code="g">year:2021</subfield><subfield code="g">number:3</subfield><subfield code="g">day:22</subfield><subfield code="g">month:07</subfield></datafield><datafield tag="856" ind1="4" ind2="1"><subfield code="u">https://doi.org/10.1007/s10092-021-00428-3</subfield><subfield code="z">lizenzpflichtig</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_OLC</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OPC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_90</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">58</subfield><subfield code="j">2021</subfield><subfield code="e">3</subfield><subfield code="b">22</subfield><subfield code="c">07</subfield></datafield></record></collection>
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