Hyers–Ulam Stability of a Second-Order Finite Difference Scheme Using a Diamond-%$\alpha %$ Difference Operator

Abstract We establish the Hyers–Ulam stability of a second-order finite difference scheme using a diamond-%$\alpha %$ difference operator for second-order non-homogeneous linear differential equations with constant coefficients. Hyers–Ulam stability constants and best stability constants are determi...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Anderson, Douglas R. [verfasserIn] Tanner, Gregory M.

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2024

Schlagwörter:	Diamond–alpha derivative Centered-difference operator Stability regions Best stability constant

Anmerkung:	© The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Übergeordnetes Werk:	Enthalten in: Qualitative theory of dynamical systems - Basel : Birkhäuser, 1999, 23(2024), 2 vom: 06. Jan.
Übergeordnetes Werk:	volume:23 ; year:2024 ; number:2 ; day:06 ; month:01

Links:	Volltext

DOI / URN:	10.1007/s12346-023-00927-4

Katalog-ID:	SPR054293855

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520			\|a Abstract We establish the Hyers–Ulam stability of a second-order finite difference scheme using a diamond-%$\alpha %$ difference operator for second-order non-homogeneous linear differential equations with constant coefficients. Hyers–Ulam stability constants and best stability constants are determined for stability regions in the parameter space. In an application of our results, we compare our difference scheme with the more common centered-difference scheme, as an approximation to secord-order differential equations.
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allfields	10.1007/s12346-023-00927-4 doi (DE-627)SPR054293855 (SPR)s12346-023-00927-4-e DE-627 ger DE-627 rakwb eng Anderson, Douglas R. verfasserin aut Hyers–Ulam Stability of a Second-Order Finite Difference Scheme Using a Diamond-%$\alpha %$ Difference Operator 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract We establish the Hyers–Ulam stability of a second-order finite difference scheme using a diamond-%$\alpha %$ difference operator for second-order non-homogeneous linear differential equations with constant coefficients. Hyers–Ulam stability constants and best stability constants are determined for stability regions in the parameter space. In an application of our results, we compare our difference scheme with the more common centered-difference scheme, as an approximation to secord-order differential equations. Diamond–alpha derivative (dpeaa)DE-He213 Centered-difference operator (dpeaa)DE-He213 Stability regions (dpeaa)DE-He213 Best stability constant (dpeaa)DE-He213 Tanner, Gregory M. aut Enthalten in Qualitative theory of dynamical systems Basel : Birkhäuser, 1999 23(2024), 2 vom: 06. Jan. (DE-627)582026512 (DE-600)2457088-6 1662-3592 nnns volume:23 year:2024 number:2 day:06 month:01 https://dx.doi.org/10.1007/s12346-023-00927-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 23 2024 2 06 01
spelling	10.1007/s12346-023-00927-4 doi (DE-627)SPR054293855 (SPR)s12346-023-00927-4-e DE-627 ger DE-627 rakwb eng Anderson, Douglas R. verfasserin aut Hyers–Ulam Stability of a Second-Order Finite Difference Scheme Using a Diamond-%$\alpha %$ Difference Operator 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract We establish the Hyers–Ulam stability of a second-order finite difference scheme using a diamond-%$\alpha %$ difference operator for second-order non-homogeneous linear differential equations with constant coefficients. Hyers–Ulam stability constants and best stability constants are determined for stability regions in the parameter space. In an application of our results, we compare our difference scheme with the more common centered-difference scheme, as an approximation to secord-order differential equations. Diamond–alpha derivative (dpeaa)DE-He213 Centered-difference operator (dpeaa)DE-He213 Stability regions (dpeaa)DE-He213 Best stability constant (dpeaa)DE-He213 Tanner, Gregory M. aut Enthalten in Qualitative theory of dynamical systems Basel : Birkhäuser, 1999 23(2024), 2 vom: 06. Jan. (DE-627)582026512 (DE-600)2457088-6 1662-3592 nnns volume:23 year:2024 number:2 day:06 month:01 https://dx.doi.org/10.1007/s12346-023-00927-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 23 2024 2 06 01
allfields_unstemmed	10.1007/s12346-023-00927-4 doi (DE-627)SPR054293855 (SPR)s12346-023-00927-4-e DE-627 ger DE-627 rakwb eng Anderson, Douglas R. verfasserin aut Hyers–Ulam Stability of a Second-Order Finite Difference Scheme Using a Diamond-%$\alpha %$ Difference Operator 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract We establish the Hyers–Ulam stability of a second-order finite difference scheme using a diamond-%$\alpha %$ difference operator for second-order non-homogeneous linear differential equations with constant coefficients. Hyers–Ulam stability constants and best stability constants are determined for stability regions in the parameter space. In an application of our results, we compare our difference scheme with the more common centered-difference scheme, as an approximation to secord-order differential equations. Diamond–alpha derivative (dpeaa)DE-He213 Centered-difference operator (dpeaa)DE-He213 Stability regions (dpeaa)DE-He213 Best stability constant (dpeaa)DE-He213 Tanner, Gregory M. aut Enthalten in Qualitative theory of dynamical systems Basel : Birkhäuser, 1999 23(2024), 2 vom: 06. Jan. (DE-627)582026512 (DE-600)2457088-6 1662-3592 nnns volume:23 year:2024 number:2 day:06 month:01 https://dx.doi.org/10.1007/s12346-023-00927-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 23 2024 2 06 01
allfieldsGer	10.1007/s12346-023-00927-4 doi (DE-627)SPR054293855 (SPR)s12346-023-00927-4-e DE-627 ger DE-627 rakwb eng Anderson, Douglas R. verfasserin aut Hyers–Ulam Stability of a Second-Order Finite Difference Scheme Using a Diamond-%$\alpha %$ Difference Operator 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract We establish the Hyers–Ulam stability of a second-order finite difference scheme using a diamond-%$\alpha %$ difference operator for second-order non-homogeneous linear differential equations with constant coefficients. Hyers–Ulam stability constants and best stability constants are determined for stability regions in the parameter space. In an application of our results, we compare our difference scheme with the more common centered-difference scheme, as an approximation to secord-order differential equations. Diamond–alpha derivative (dpeaa)DE-He213 Centered-difference operator (dpeaa)DE-He213 Stability regions (dpeaa)DE-He213 Best stability constant (dpeaa)DE-He213 Tanner, Gregory M. aut Enthalten in Qualitative theory of dynamical systems Basel : Birkhäuser, 1999 23(2024), 2 vom: 06. Jan. (DE-627)582026512 (DE-600)2457088-6 1662-3592 nnns volume:23 year:2024 number:2 day:06 month:01 https://dx.doi.org/10.1007/s12346-023-00927-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 23 2024 2 06 01
allfieldsSound	10.1007/s12346-023-00927-4 doi (DE-627)SPR054293855 (SPR)s12346-023-00927-4-e DE-627 ger DE-627 rakwb eng Anderson, Douglas R. verfasserin aut Hyers–Ulam Stability of a Second-Order Finite Difference Scheme Using a Diamond-%$\alpha %$ Difference Operator 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract We establish the Hyers–Ulam stability of a second-order finite difference scheme using a diamond-%$\alpha %$ difference operator for second-order non-homogeneous linear differential equations with constant coefficients. Hyers–Ulam stability constants and best stability constants are determined for stability regions in the parameter space. In an application of our results, we compare our difference scheme with the more common centered-difference scheme, as an approximation to secord-order differential equations. Diamond–alpha derivative (dpeaa)DE-He213 Centered-difference operator (dpeaa)DE-He213 Stability regions (dpeaa)DE-He213 Best stability constant (dpeaa)DE-He213 Tanner, Gregory M. aut Enthalten in Qualitative theory of dynamical systems Basel : Birkhäuser, 1999 23(2024), 2 vom: 06. Jan. (DE-627)582026512 (DE-600)2457088-6 1662-3592 nnns volume:23 year:2024 number:2 day:06 month:01 https://dx.doi.org/10.1007/s12346-023-00927-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 23 2024 2 06 01
language	English
source	Enthalten in Qualitative theory of dynamical systems 23(2024), 2 vom: 06. Jan. volume:23 year:2024 number:2 day:06 month:01
sourceStr	Enthalten in Qualitative theory of dynamical systems 23(2024), 2 vom: 06. Jan. volume:23 year:2024 number:2 day:06 month:01
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Diamond–alpha derivative Centered-difference operator Stability regions Best stability constant
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container_title	Qualitative theory of dynamical systems
authorswithroles_txt_mv	Anderson, Douglas R. @@aut@@ Tanner, Gregory M. @@aut@@
publishDateDaySort_date	2024-01-06T00:00:00Z
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author	Anderson, Douglas R.
spellingShingle	Anderson, Douglas R. misc Diamond–alpha derivative misc Centered-difference operator misc Stability regions misc Best stability constant Hyers–Ulam Stability of a Second-Order Finite Difference Scheme Using a Diamond-%$\alpha %$ Difference Operator
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topic_title	Hyers–Ulam Stability of a Second-Order Finite Difference Scheme Using a Diamond-%$\alpha %$ Difference Operator Diamond–alpha derivative (dpeaa)DE-He213 Centered-difference operator (dpeaa)DE-He213 Stability regions (dpeaa)DE-He213 Best stability constant (dpeaa)DE-He213
topic	misc Diamond–alpha derivative misc Centered-difference operator misc Stability regions misc Best stability constant
topic_unstemmed	misc Diamond–alpha derivative misc Centered-difference operator misc Stability regions misc Best stability constant
topic_browse	misc Diamond–alpha derivative misc Centered-difference operator misc Stability regions misc Best stability constant
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title	Hyers–Ulam Stability of a Second-Order Finite Difference Scheme Using a Diamond-%$\alpha %$ Difference Operator
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title_full	Hyers–Ulam Stability of a Second-Order Finite Difference Scheme Using a Diamond-%$\alpha %$ Difference Operator
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author_browse	Anderson, Douglas R. Tanner, Gregory M.
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title_sort	hyers–ulam stability of a second-order finite difference scheme using a diamond-%$\alpha %$ difference operator
title_auth	Hyers–Ulam Stability of a Second-Order Finite Difference Scheme Using a Diamond-%$\alpha %$ Difference Operator
abstract	Abstract We establish the Hyers–Ulam stability of a second-order finite difference scheme using a diamond-%$\alpha %$ difference operator for second-order non-homogeneous linear differential equations with constant coefficients. Hyers–Ulam stability constants and best stability constants are determined for stability regions in the parameter space. In an application of our results, we compare our difference scheme with the more common centered-difference scheme, as an approximation to secord-order differential equations. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
abstractGer	Abstract We establish the Hyers–Ulam stability of a second-order finite difference scheme using a diamond-%$\alpha %$ difference operator for second-order non-homogeneous linear differential equations with constant coefficients. Hyers–Ulam stability constants and best stability constants are determined for stability regions in the parameter space. In an application of our results, we compare our difference scheme with the more common centered-difference scheme, as an approximation to secord-order differential equations. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
abstract_unstemmed	Abstract We establish the Hyers–Ulam stability of a second-order finite difference scheme using a diamond-%$\alpha %$ difference operator for second-order non-homogeneous linear differential equations with constant coefficients. Hyers–Ulam stability constants and best stability constants are determined for stability regions in the parameter space. In an application of our results, we compare our difference scheme with the more common centered-difference scheme, as an approximation to secord-order differential equations. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
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title_short	Hyers–Ulam Stability of a Second-Order Finite Difference Scheme Using a Diamond-%$\alpha %$ Difference Operator
url	https://dx.doi.org/10.1007/s12346-023-00927-4
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doi_str	10.1007/s12346-023-00927-4
up_date	2024-07-04T00:55:03.216Z
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Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract We establish the Hyers–Ulam stability of a second-order finite difference scheme using a diamond-%$\alpha %$ difference operator for second-order non-homogeneous linear differential equations with constant coefficients. Hyers–Ulam stability constants and best stability constants are determined for stability regions in the parameter space. In an application of our results, we compare our difference scheme with the more common centered-difference scheme, as an approximation to secord-order differential equations.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Diamond–alpha derivative</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Centered-difference operator</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Stability regions</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Best stability constant</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Tanner, Gregory M.</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Qualitative theory of dynamical systems</subfield><subfield code="d">Basel : Birkhäuser, 1999</subfield><subfield code="g">23(2024), 2 vom: 06. 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