High-Order Dissipation-Preserving Methods for Nonlinear Fractional Generalized Wave Equations

In this paper, we construct and analyze a class of high-order and dissipation-preserving schemes for the nonlinear space fractional generalized wave equations by the newly introduced scalar auxiliary variable (SAV) technique. The system is discretized by a fourth-order Riesz fractional difference op...
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Gespeichert in:

Autor*in:	Yu Li [verfasserIn] Wei Shan [verfasserIn] Yanming Zhang [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2022

Schlagwörter:	nonlinear fractional generalized wave equation dissipation-preserving scheme scalar auxiliary variable approach Lubich difference operator

Übergeordnetes Werk:	In: Fractal and Fractional - MDPI AG, 2018, 6(2022), 5, p 264
Übergeordnetes Werk:	volume:6 ; year:2022 ; number:5, p 264

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.3390/fractalfract6050264

Katalog-ID:	DOAJ04079704X

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520			\|a In this paper, we construct and analyze a class of high-order and dissipation-preserving schemes for the nonlinear space fractional generalized wave equations by the newly introduced scalar auxiliary variable (SAV) technique. The system is discretized by a fourth-order Riesz fractional difference operator in spatial discretization and the collocation methods in the temporal direction. Not only can the present method achieve fourth-order accuracy in the spatial direction and arbitrarily high-order accuracy in the temporal direction, but it also has long-time computing stability. Then, the unconditional discrete energy dissipation law of the present numerical schemes is proved. Finally, some numerical experiments are provided to certify the efficiency and the structure-preserving properties of the proposed schemes.
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allfields	10.3390/fractalfract6050264 doi (DE-627)DOAJ04079704X (DE-599)DOAJ0190c1117ae64f5ea602eb85f5e4ded0 DE-627 ger DE-627 rakwb eng QC310.15-319 QA1-939 QA299.6-433 Yu Li verfasserin aut High-Order Dissipation-Preserving Methods for Nonlinear Fractional Generalized Wave Equations 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper, we construct and analyze a class of high-order and dissipation-preserving schemes for the nonlinear space fractional generalized wave equations by the newly introduced scalar auxiliary variable (SAV) technique. The system is discretized by a fourth-order Riesz fractional difference operator in spatial discretization and the collocation methods in the temporal direction. Not only can the present method achieve fourth-order accuracy in the spatial direction and arbitrarily high-order accuracy in the temporal direction, but it also has long-time computing stability. Then, the unconditional discrete energy dissipation law of the present numerical schemes is proved. Finally, some numerical experiments are provided to certify the efficiency and the structure-preserving properties of the proposed schemes. nonlinear fractional generalized wave equation dissipation-preserving scheme scalar auxiliary variable approach Lubich difference operator Thermodynamics Mathematics Analysis Wei Shan verfasserin aut Yanming Zhang verfasserin aut In Fractal and Fractional MDPI AG, 2018 6(2022), 5, p 264 (DE-627)897435656 (DE-600)2905371-7 25043110 nnns volume:6 year:2022 number:5, p 264 https://doi.org/10.3390/fractalfract6050264 kostenfrei https://doaj.org/article/0190c1117ae64f5ea602eb85f5e4ded0 kostenfrei https://www.mdpi.com/2504-3110/6/5/264 kostenfrei https://doaj.org/toc/2504-3110 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 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_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 6 2022 5, p 264
spelling	10.3390/fractalfract6050264 doi (DE-627)DOAJ04079704X (DE-599)DOAJ0190c1117ae64f5ea602eb85f5e4ded0 DE-627 ger DE-627 rakwb eng QC310.15-319 QA1-939 QA299.6-433 Yu Li verfasserin aut High-Order Dissipation-Preserving Methods for Nonlinear Fractional Generalized Wave Equations 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper, we construct and analyze a class of high-order and dissipation-preserving schemes for the nonlinear space fractional generalized wave equations by the newly introduced scalar auxiliary variable (SAV) technique. The system is discretized by a fourth-order Riesz fractional difference operator in spatial discretization and the collocation methods in the temporal direction. Not only can the present method achieve fourth-order accuracy in the spatial direction and arbitrarily high-order accuracy in the temporal direction, but it also has long-time computing stability. Then, the unconditional discrete energy dissipation law of the present numerical schemes is proved. Finally, some numerical experiments are provided to certify the efficiency and the structure-preserving properties of the proposed schemes. nonlinear fractional generalized wave equation dissipation-preserving scheme scalar auxiliary variable approach Lubich difference operator Thermodynamics Mathematics Analysis Wei Shan verfasserin aut Yanming Zhang verfasserin aut In Fractal and Fractional MDPI AG, 2018 6(2022), 5, p 264 (DE-627)897435656 (DE-600)2905371-7 25043110 nnns volume:6 year:2022 number:5, p 264 https://doi.org/10.3390/fractalfract6050264 kostenfrei https://doaj.org/article/0190c1117ae64f5ea602eb85f5e4ded0 kostenfrei https://www.mdpi.com/2504-3110/6/5/264 kostenfrei https://doaj.org/toc/2504-3110 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 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_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 6 2022 5, p 264
allfields_unstemmed	10.3390/fractalfract6050264 doi (DE-627)DOAJ04079704X (DE-599)DOAJ0190c1117ae64f5ea602eb85f5e4ded0 DE-627 ger DE-627 rakwb eng QC310.15-319 QA1-939 QA299.6-433 Yu Li verfasserin aut High-Order Dissipation-Preserving Methods for Nonlinear Fractional Generalized Wave Equations 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper, we construct and analyze a class of high-order and dissipation-preserving schemes for the nonlinear space fractional generalized wave equations by the newly introduced scalar auxiliary variable (SAV) technique. The system is discretized by a fourth-order Riesz fractional difference operator in spatial discretization and the collocation methods in the temporal direction. Not only can the present method achieve fourth-order accuracy in the spatial direction and arbitrarily high-order accuracy in the temporal direction, but it also has long-time computing stability. Then, the unconditional discrete energy dissipation law of the present numerical schemes is proved. Finally, some numerical experiments are provided to certify the efficiency and the structure-preserving properties of the proposed schemes. nonlinear fractional generalized wave equation dissipation-preserving scheme scalar auxiliary variable approach Lubich difference operator Thermodynamics Mathematics Analysis Wei Shan verfasserin aut Yanming Zhang verfasserin aut In Fractal and Fractional MDPI AG, 2018 6(2022), 5, p 264 (DE-627)897435656 (DE-600)2905371-7 25043110 nnns volume:6 year:2022 number:5, p 264 https://doi.org/10.3390/fractalfract6050264 kostenfrei https://doaj.org/article/0190c1117ae64f5ea602eb85f5e4ded0 kostenfrei https://www.mdpi.com/2504-3110/6/5/264 kostenfrei https://doaj.org/toc/2504-3110 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 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_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 6 2022 5, p 264
allfieldsGer	10.3390/fractalfract6050264 doi (DE-627)DOAJ04079704X (DE-599)DOAJ0190c1117ae64f5ea602eb85f5e4ded0 DE-627 ger DE-627 rakwb eng QC310.15-319 QA1-939 QA299.6-433 Yu Li verfasserin aut High-Order Dissipation-Preserving Methods for Nonlinear Fractional Generalized Wave Equations 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper, we construct and analyze a class of high-order and dissipation-preserving schemes for the nonlinear space fractional generalized wave equations by the newly introduced scalar auxiliary variable (SAV) technique. The system is discretized by a fourth-order Riesz fractional difference operator in spatial discretization and the collocation methods in the temporal direction. Not only can the present method achieve fourth-order accuracy in the spatial direction and arbitrarily high-order accuracy in the temporal direction, but it also has long-time computing stability. Then, the unconditional discrete energy dissipation law of the present numerical schemes is proved. Finally, some numerical experiments are provided to certify the efficiency and the structure-preserving properties of the proposed schemes. nonlinear fractional generalized wave equation dissipation-preserving scheme scalar auxiliary variable approach Lubich difference operator Thermodynamics Mathematics Analysis Wei Shan verfasserin aut Yanming Zhang verfasserin aut In Fractal and Fractional MDPI AG, 2018 6(2022), 5, p 264 (DE-627)897435656 (DE-600)2905371-7 25043110 nnns volume:6 year:2022 number:5, p 264 https://doi.org/10.3390/fractalfract6050264 kostenfrei https://doaj.org/article/0190c1117ae64f5ea602eb85f5e4ded0 kostenfrei https://www.mdpi.com/2504-3110/6/5/264 kostenfrei https://doaj.org/toc/2504-3110 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 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_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 6 2022 5, p 264
allfieldsSound	10.3390/fractalfract6050264 doi (DE-627)DOAJ04079704X (DE-599)DOAJ0190c1117ae64f5ea602eb85f5e4ded0 DE-627 ger DE-627 rakwb eng QC310.15-319 QA1-939 QA299.6-433 Yu Li verfasserin aut High-Order Dissipation-Preserving Methods for Nonlinear Fractional Generalized Wave Equations 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper, we construct and analyze a class of high-order and dissipation-preserving schemes for the nonlinear space fractional generalized wave equations by the newly introduced scalar auxiliary variable (SAV) technique. The system is discretized by a fourth-order Riesz fractional difference operator in spatial discretization and the collocation methods in the temporal direction. Not only can the present method achieve fourth-order accuracy in the spatial direction and arbitrarily high-order accuracy in the temporal direction, but it also has long-time computing stability. Then, the unconditional discrete energy dissipation law of the present numerical schemes is proved. Finally, some numerical experiments are provided to certify the efficiency and the structure-preserving properties of the proposed schemes. nonlinear fractional generalized wave equation dissipation-preserving scheme scalar auxiliary variable approach Lubich difference operator Thermodynamics Mathematics Analysis Wei Shan verfasserin aut Yanming Zhang verfasserin aut In Fractal and Fractional MDPI AG, 2018 6(2022), 5, p 264 (DE-627)897435656 (DE-600)2905371-7 25043110 nnns volume:6 year:2022 number:5, p 264 https://doi.org/10.3390/fractalfract6050264 kostenfrei https://doaj.org/article/0190c1117ae64f5ea602eb85f5e4ded0 kostenfrei https://www.mdpi.com/2504-3110/6/5/264 kostenfrei https://doaj.org/toc/2504-3110 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 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_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 6 2022 5, p 264
language	English
source	In Fractal and Fractional 6(2022), 5, p 264 volume:6 year:2022 number:5, p 264
sourceStr	In Fractal and Fractional 6(2022), 5, p 264 volume:6 year:2022 number:5, p 264
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	nonlinear fractional generalized wave equation dissipation-preserving scheme scalar auxiliary variable approach Lubich difference operator Thermodynamics Mathematics Analysis
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authorswithroles_txt_mv	Yu Li @@aut@@ Wei Shan @@aut@@ Yanming Zhang @@aut@@
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callnumber-first	Q - Science
author	Yu Li
spellingShingle	Yu Li misc QC310.15-319 misc QA1-939 misc QA299.6-433 misc nonlinear fractional generalized wave equation misc dissipation-preserving scheme misc scalar auxiliary variable approach misc Lubich difference operator misc Thermodynamics misc Mathematics misc Analysis High-Order Dissipation-Preserving Methods for Nonlinear Fractional Generalized Wave Equations
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topic_title	QC310.15-319 QA1-939 QA299.6-433 High-Order Dissipation-Preserving Methods for Nonlinear Fractional Generalized Wave Equations nonlinear fractional generalized wave equation dissipation-preserving scheme scalar auxiliary variable approach Lubich difference operator
topic	misc QC310.15-319 misc QA1-939 misc QA299.6-433 misc nonlinear fractional generalized wave equation misc dissipation-preserving scheme misc scalar auxiliary variable approach misc Lubich difference operator misc Thermodynamics misc Mathematics misc Analysis
topic_unstemmed	misc QC310.15-319 misc QA1-939 misc QA299.6-433 misc nonlinear fractional generalized wave equation misc dissipation-preserving scheme misc scalar auxiliary variable approach misc Lubich difference operator misc Thermodynamics misc Mathematics misc Analysis
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title	High-Order Dissipation-Preserving Methods for Nonlinear Fractional Generalized Wave Equations
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title_sort	high-order dissipation-preserving methods for nonlinear fractional generalized wave equations
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title_auth	High-Order Dissipation-Preserving Methods for Nonlinear Fractional Generalized Wave Equations
abstract	In this paper, we construct and analyze a class of high-order and dissipation-preserving schemes for the nonlinear space fractional generalized wave equations by the newly introduced scalar auxiliary variable (SAV) technique. The system is discretized by a fourth-order Riesz fractional difference operator in spatial discretization and the collocation methods in the temporal direction. Not only can the present method achieve fourth-order accuracy in the spatial direction and arbitrarily high-order accuracy in the temporal direction, but it also has long-time computing stability. Then, the unconditional discrete energy dissipation law of the present numerical schemes is proved. Finally, some numerical experiments are provided to certify the efficiency and the structure-preserving properties of the proposed schemes.
abstractGer	In this paper, we construct and analyze a class of high-order and dissipation-preserving schemes for the nonlinear space fractional generalized wave equations by the newly introduced scalar auxiliary variable (SAV) technique. The system is discretized by a fourth-order Riesz fractional difference operator in spatial discretization and the collocation methods in the temporal direction. Not only can the present method achieve fourth-order accuracy in the spatial direction and arbitrarily high-order accuracy in the temporal direction, but it also has long-time computing stability. Then, the unconditional discrete energy dissipation law of the present numerical schemes is proved. Finally, some numerical experiments are provided to certify the efficiency and the structure-preserving properties of the proposed schemes.
abstract_unstemmed	In this paper, we construct and analyze a class of high-order and dissipation-preserving schemes for the nonlinear space fractional generalized wave equations by the newly introduced scalar auxiliary variable (SAV) technique. The system is discretized by a fourth-order Riesz fractional difference operator in spatial discretization and the collocation methods in the temporal direction. Not only can the present method achieve fourth-order accuracy in the spatial direction and arbitrarily high-order accuracy in the temporal direction, but it also has long-time computing stability. Then, the unconditional discrete energy dissipation law of the present numerical schemes is proved. Finally, some numerical experiments are provided to certify the efficiency and the structure-preserving properties of the proposed schemes.
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title_short	High-Order Dissipation-Preserving Methods for Nonlinear Fractional Generalized Wave Equations
url	https://doi.org/10.3390/fractalfract6050264 https://doaj.org/article/0190c1117ae64f5ea602eb85f5e4ded0 https://www.mdpi.com/2504-3110/6/5/264 https://doaj.org/toc/2504-3110
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High-Order Dissipation-Preserving Methods for Nonlinear Fractional Generalized Wave Equations

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