Local error estimates of the fourth-order compact difference scheme for a time-fractional diffusion-wave equation

This paper considers the numerical approximation for the time-fractional diffusion-wave equation with the order α ∈ ( 1 , 2 ) , whose solution behaves a weak singular...
Ausführliche Beschreibung

This paper considers the numerical approximation for the time-fractional diffusion-wave equation with the order α ∈ ( 1 , 2 ) , whose solution behaves a weak singularity at t = 0 . To construct the high-order scheme, the intermediate variable w = D t α / 2 ( u − t ϕ ˜ ) is introduced, then we can rewrite the original problem as a coupled system, where u is the solution of the time-fractional diffusion-wave equation and ϕ ˜ = u t ( x , 0 ) . By using the L1 scheme on graded meshes in temporal direction and the compact difference scheme in spatial direction, a fully discrete scheme is constructed for the coupled system. Furthermore, the stability and the local error estimate of the proposed scheme is given. Finally, numerical examples are presented to verify the accuracy and efficiency of the proposed method. Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Zhang, Dan [verfasserIn] An, Na [verfasserIn] Huang, Chaobao [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2023

Schlagwörter:	Time-fractional diffusion-wave equations Compact difference schemes Local error estimates Graded meshes

Übergeordnetes Werk:	Enthalten in: Computers and mathematics with applications - Amsterdam [u.a.] : Elsevier Science, 1975, 142, Seite 283-292
Übergeordnetes Werk:	volume:142 ; pages:283-292

DOI / URN:	10.1016/j.camwa.2023.05.009

Katalog-ID:	ELV010017801

Internformat


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100	1		\|a Zhang, Dan \|e verfasserin \|4 aut
245	1	0	\|a Local error estimates of the fourth-order compact difference scheme for a time-fractional diffusion-wave equation
264		1	\|c 2023
336			\|a nicht spezifiziert \|b zzz \|2 rdacontent
337			\|a Computermedien \|b c \|2 rdamedia
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520			\|a This paper considers the numerical approximation for the time-fractional diffusion-wave equation with the order α ∈ ( 1 , 2 ) , whose solution behaves a weak singularity at t = 0 . To construct the high-order scheme, the intermediate variable w = D t α / 2 ( u − t ϕ ˜ ) is introduced, then we can rewrite the original problem as a coupled system, where u is the solution of the time-fractional diffusion-wave equation and ϕ ˜ = u t ( x , 0 ) . By using the L1 scheme on graded meshes in temporal direction and the compact difference scheme in spatial direction, a fully discrete scheme is constructed for the coupled system. Furthermore, the stability and the local error estimate of the proposed scheme is given. Finally, numerical examples are presented to verify the accuracy and efficiency of the proposed method.
650		4	\|a Time-fractional diffusion-wave equations
650		4	\|a Compact difference schemes
650		4	\|a Local error estimates
650		4	\|a Graded meshes
700	1		\|a An, Na \|e verfasserin \|4 aut
700	1		\|a Huang, Chaobao \|e verfasserin \|4 aut
773	0	8	\|i Enthalten in \|t Computers and mathematics with applications \|d Amsterdam [u.a.] : Elsevier Science, 1975 \|g 142, Seite 283-292 \|h Online-Ressource \|w (DE-627)320435121 \|w (DE-600)2004251-6 \|w (DE-576)259271225 \|x 1873-7668 \|7 nnns
773	1	8	\|g volume:142 \|g pages:283-292
912			\|a GBV_USEFLAG_U
912			\|a SYSFLAG_U
912			\|a GBV_ELV
912			\|a SSG-OPC-MAT
912			\|a GBV_ILN_20
912			\|a GBV_ILN_22
912			\|a GBV_ILN_23
912			\|a GBV_ILN_24
912			\|a GBV_ILN_31
912			\|a GBV_ILN_32
912			\|a GBV_ILN_40
912			\|a GBV_ILN_60
912			\|a GBV_ILN_62
912			\|a GBV_ILN_65
912			\|a GBV_ILN_69
912			\|a GBV_ILN_70
912			\|a GBV_ILN_73
912			\|a GBV_ILN_74
912			\|a GBV_ILN_90
912			\|a GBV_ILN_95
912			\|a GBV_ILN_100
912			\|a GBV_ILN_101
912			\|a GBV_ILN_105
912			\|a GBV_ILN_110
912			\|a GBV_ILN_150
912			\|a GBV_ILN_151
912			\|a GBV_ILN_187
912			\|a GBV_ILN_213
912			\|a GBV_ILN_224
912			\|a GBV_ILN_230
912			\|a GBV_ILN_370
912			\|a GBV_ILN_602
912			\|a GBV_ILN_702
912			\|a GBV_ILN_2001
912			\|a GBV_ILN_2003
912			\|a GBV_ILN_2004
912			\|a GBV_ILN_2005
912			\|a GBV_ILN_2007
912			\|a GBV_ILN_2008
912			\|a GBV_ILN_2009
912			\|a GBV_ILN_2010
912			\|a GBV_ILN_2011
912			\|a GBV_ILN_2014
912			\|a GBV_ILN_2015
912			\|a GBV_ILN_2020
912			\|a GBV_ILN_2021
912			\|a GBV_ILN_2025
912			\|a GBV_ILN_2026
912			\|a GBV_ILN_2027
912			\|a GBV_ILN_2034
912			\|a GBV_ILN_2044
912			\|a GBV_ILN_2048
912			\|a GBV_ILN_2049
912			\|a GBV_ILN_2050
912			\|a GBV_ILN_2055
912			\|a GBV_ILN_2056
912			\|a GBV_ILN_2059
912			\|a GBV_ILN_2061
912			\|a GBV_ILN_2064
912			\|a GBV_ILN_2088
912			\|a GBV_ILN_2106
912			\|a GBV_ILN_2110
912			\|a GBV_ILN_2111
912			\|a GBV_ILN_2112
912			\|a GBV_ILN_2122
912			\|a GBV_ILN_2129
912			\|a GBV_ILN_2143
912			\|a GBV_ILN_2152
912			\|a GBV_ILN_2153
912			\|a GBV_ILN_2190
912			\|a GBV_ILN_2232
912			\|a GBV_ILN_2336
912			\|a GBV_ILN_2470
912			\|a GBV_ILN_2507
912			\|a GBV_ILN_4012
912			\|a GBV_ILN_4035
912			\|a GBV_ILN_4037
912			\|a GBV_ILN_4112
912			\|a GBV_ILN_4125
912			\|a GBV_ILN_4126
912			\|a GBV_ILN_4242
912			\|a GBV_ILN_4249
912			\|a GBV_ILN_4251
912			\|a GBV_ILN_4305
912			\|a GBV_ILN_4306
912			\|a GBV_ILN_4307
912			\|a GBV_ILN_4313
912			\|a GBV_ILN_4322
912			\|a GBV_ILN_4323
912			\|a GBV_ILN_4324
912			\|a GBV_ILN_4325
912			\|a GBV_ILN_4326
912			\|a GBV_ILN_4333
912			\|a GBV_ILN_4334
912			\|a GBV_ILN_4335
912			\|a GBV_ILN_4338
912			\|a GBV_ILN_4367
912			\|a GBV_ILN_4393
912			\|a GBV_ILN_4700
936	b	k	\|a 31.80 \|j Angewandte Mathematik \|q VZ
936	b	k	\|a 54.80 \|j Angewandte Informatik \|q VZ
951			\|a AR
952			\|d 142 \|h 283-292

Indexfelder

author_variant	d z dz n a na c h ch
matchkey_str	article:18737668:2023----::oaerrsiaeoteorhrecmatifrneceeoaierci
hierarchy_sort_str	2023
bklnumber	31.80 54.80
publishDate	2023
allfields	10.1016/j.camwa.2023.05.009 doi (DE-627)ELV010017801 (ELSEVIER)S0898-1221(23)00208-0 DE-627 ger DE-627 rda eng 510 004 VZ 31.80 bkl 54.80 bkl Zhang, Dan verfasserin aut Local error estimates of the fourth-order compact difference scheme for a time-fractional diffusion-wave equation 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier This paper considers the numerical approximation for the time-fractional diffusion-wave equation with the order α ∈ ( 1 , 2 ) , whose solution behaves a weak singularity at t = 0 . To construct the high-order scheme, the intermediate variable w = D t α / 2 ( u − t ϕ ˜ ) is introduced, then we can rewrite the original problem as a coupled system, where u is the solution of the time-fractional diffusion-wave equation and ϕ ˜ = u t ( x , 0 ) . By using the L1 scheme on graded meshes in temporal direction and the compact difference scheme in spatial direction, a fully discrete scheme is constructed for the coupled system. Furthermore, the stability and the local error estimate of the proposed scheme is given. Finally, numerical examples are presented to verify the accuracy and efficiency of the proposed method. Time-fractional diffusion-wave equations Compact difference schemes Local error estimates Graded meshes An, Na verfasserin aut Huang, Chaobao verfasserin aut Enthalten in Computers and mathematics with applications Amsterdam [u.a.] : Elsevier Science, 1975 142, Seite 283-292 Online-Ressource (DE-627)320435121 (DE-600)2004251-6 (DE-576)259271225 1873-7668 nnns volume:142 pages:283-292 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 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_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2008 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_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.80 Angewandte Mathematik VZ 54.80 Angewandte Informatik VZ AR 142 283-292
spelling	10.1016/j.camwa.2023.05.009 doi (DE-627)ELV010017801 (ELSEVIER)S0898-1221(23)00208-0 DE-627 ger DE-627 rda eng 510 004 VZ 31.80 bkl 54.80 bkl Zhang, Dan verfasserin aut Local error estimates of the fourth-order compact difference scheme for a time-fractional diffusion-wave equation 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier This paper considers the numerical approximation for the time-fractional diffusion-wave equation with the order α ∈ ( 1 , 2 ) , whose solution behaves a weak singularity at t = 0 . To construct the high-order scheme, the intermediate variable w = D t α / 2 ( u − t ϕ ˜ ) is introduced, then we can rewrite the original problem as a coupled system, where u is the solution of the time-fractional diffusion-wave equation and ϕ ˜ = u t ( x , 0 ) . By using the L1 scheme on graded meshes in temporal direction and the compact difference scheme in spatial direction, a fully discrete scheme is constructed for the coupled system. Furthermore, the stability and the local error estimate of the proposed scheme is given. Finally, numerical examples are presented to verify the accuracy and efficiency of the proposed method. Time-fractional diffusion-wave equations Compact difference schemes Local error estimates Graded meshes An, Na verfasserin aut Huang, Chaobao verfasserin aut Enthalten in Computers and mathematics with applications Amsterdam [u.a.] : Elsevier Science, 1975 142, Seite 283-292 Online-Ressource (DE-627)320435121 (DE-600)2004251-6 (DE-576)259271225 1873-7668 nnns volume:142 pages:283-292 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 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_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2008 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_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.80 Angewandte Mathematik VZ 54.80 Angewandte Informatik VZ AR 142 283-292
allfields_unstemmed	10.1016/j.camwa.2023.05.009 doi (DE-627)ELV010017801 (ELSEVIER)S0898-1221(23)00208-0 DE-627 ger DE-627 rda eng 510 004 VZ 31.80 bkl 54.80 bkl Zhang, Dan verfasserin aut Local error estimates of the fourth-order compact difference scheme for a time-fractional diffusion-wave equation 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier This paper considers the numerical approximation for the time-fractional diffusion-wave equation with the order α ∈ ( 1 , 2 ) , whose solution behaves a weak singularity at t = 0 . To construct the high-order scheme, the intermediate variable w = D t α / 2 ( u − t ϕ ˜ ) is introduced, then we can rewrite the original problem as a coupled system, where u is the solution of the time-fractional diffusion-wave equation and ϕ ˜ = u t ( x , 0 ) . By using the L1 scheme on graded meshes in temporal direction and the compact difference scheme in spatial direction, a fully discrete scheme is constructed for the coupled system. Furthermore, the stability and the local error estimate of the proposed scheme is given. Finally, numerical examples are presented to verify the accuracy and efficiency of the proposed method. Time-fractional diffusion-wave equations Compact difference schemes Local error estimates Graded meshes An, Na verfasserin aut Huang, Chaobao verfasserin aut Enthalten in Computers and mathematics with applications Amsterdam [u.a.] : Elsevier Science, 1975 142, Seite 283-292 Online-Ressource (DE-627)320435121 (DE-600)2004251-6 (DE-576)259271225 1873-7668 nnns volume:142 pages:283-292 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 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_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2008 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_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.80 Angewandte Mathematik VZ 54.80 Angewandte Informatik VZ AR 142 283-292
allfieldsGer	10.1016/j.camwa.2023.05.009 doi (DE-627)ELV010017801 (ELSEVIER)S0898-1221(23)00208-0 DE-627 ger DE-627 rda eng 510 004 VZ 31.80 bkl 54.80 bkl Zhang, Dan verfasserin aut Local error estimates of the fourth-order compact difference scheme for a time-fractional diffusion-wave equation 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier This paper considers the numerical approximation for the time-fractional diffusion-wave equation with the order α ∈ ( 1 , 2 ) , whose solution behaves a weak singularity at t = 0 . To construct the high-order scheme, the intermediate variable w = D t α / 2 ( u − t ϕ ˜ ) is introduced, then we can rewrite the original problem as a coupled system, where u is the solution of the time-fractional diffusion-wave equation and ϕ ˜ = u t ( x , 0 ) . By using the L1 scheme on graded meshes in temporal direction and the compact difference scheme in spatial direction, a fully discrete scheme is constructed for the coupled system. Furthermore, the stability and the local error estimate of the proposed scheme is given. Finally, numerical examples are presented to verify the accuracy and efficiency of the proposed method. Time-fractional diffusion-wave equations Compact difference schemes Local error estimates Graded meshes An, Na verfasserin aut Huang, Chaobao verfasserin aut Enthalten in Computers and mathematics with applications Amsterdam [u.a.] : Elsevier Science, 1975 142, Seite 283-292 Online-Ressource (DE-627)320435121 (DE-600)2004251-6 (DE-576)259271225 1873-7668 nnns volume:142 pages:283-292 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 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_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2008 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_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.80 Angewandte Mathematik VZ 54.80 Angewandte Informatik VZ AR 142 283-292
allfieldsSound	10.1016/j.camwa.2023.05.009 doi (DE-627)ELV010017801 (ELSEVIER)S0898-1221(23)00208-0 DE-627 ger DE-627 rda eng 510 004 VZ 31.80 bkl 54.80 bkl Zhang, Dan verfasserin aut Local error estimates of the fourth-order compact difference scheme for a time-fractional diffusion-wave equation 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier This paper considers the numerical approximation for the time-fractional diffusion-wave equation with the order α ∈ ( 1 , 2 ) , whose solution behaves a weak singularity at t = 0 . To construct the high-order scheme, the intermediate variable w = D t α / 2 ( u − t ϕ ˜ ) is introduced, then we can rewrite the original problem as a coupled system, where u is the solution of the time-fractional diffusion-wave equation and ϕ ˜ = u t ( x , 0 ) . By using the L1 scheme on graded meshes in temporal direction and the compact difference scheme in spatial direction, a fully discrete scheme is constructed for the coupled system. Furthermore, the stability and the local error estimate of the proposed scheme is given. Finally, numerical examples are presented to verify the accuracy and efficiency of the proposed method. Time-fractional diffusion-wave equations Compact difference schemes Local error estimates Graded meshes An, Na verfasserin aut Huang, Chaobao verfasserin aut Enthalten in Computers and mathematics with applications Amsterdam [u.a.] : Elsevier Science, 1975 142, Seite 283-292 Online-Ressource (DE-627)320435121 (DE-600)2004251-6 (DE-576)259271225 1873-7668 nnns volume:142 pages:283-292 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 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_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2008 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_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.80 Angewandte Mathematik VZ 54.80 Angewandte Informatik VZ AR 142 283-292
language	English
source	Enthalten in Computers and mathematics with applications 142, Seite 283-292 volume:142 pages:283-292
sourceStr	Enthalten in Computers and mathematics with applications 142, Seite 283-292 volume:142 pages:283-292
format_phy_str_mv	Article
bklname	Angewandte Mathematik Angewandte Informatik
institution	findex.gbv.de
topic_facet	Time-fractional diffusion-wave equations Compact difference schemes Local error estimates Graded meshes
dewey-raw	510
isfreeaccess_bool	false
container_title	Computers and mathematics with applications
authorswithroles_txt_mv	Zhang, Dan @@aut@@ An, Na @@aut@@ Huang, Chaobao @@aut@@
publishDateDaySort_date	2023-01-01T00:00:00Z
hierarchy_top_id	320435121
dewey-sort	3510
id	ELV010017801
language_de	englisch
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author	Zhang, Dan
spellingShingle	Zhang, Dan ddc 510 bkl 31.80 bkl 54.80 misc Time-fractional diffusion-wave equations misc Compact difference schemes misc Local error estimates misc Graded meshes Local error estimates of the fourth-order compact difference scheme for a time-fractional diffusion-wave equation
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topic_title	510 004 VZ 31.80 bkl 54.80 bkl Local error estimates of the fourth-order compact difference scheme for a time-fractional diffusion-wave equation Time-fractional diffusion-wave equations Compact difference schemes Local error estimates Graded meshes
topic	ddc 510 bkl 31.80 bkl 54.80 misc Time-fractional diffusion-wave equations misc Compact difference schemes misc Local error estimates misc Graded meshes
topic_unstemmed	ddc 510 bkl 31.80 bkl 54.80 misc Time-fractional diffusion-wave equations misc Compact difference schemes misc Local error estimates misc Graded meshes
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title	Local error estimates of the fourth-order compact difference scheme for a time-fractional diffusion-wave equation
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title_full	Local error estimates of the fourth-order compact difference scheme for a time-fractional diffusion-wave equation
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title_sort	local error estimates of the fourth-order compact difference scheme for a time-fractional diffusion-wave equation
title_auth	Local error estimates of the fourth-order compact difference scheme for a time-fractional diffusion-wave equation
abstract	This paper considers the numerical approximation for the time-fractional diffusion-wave equation with the order α ∈ ( 1 , 2 ) , whose solution behaves a weak singularity at t = 0 . To construct the high-order scheme, the intermediate variable w = D t α / 2 ( u − t ϕ ˜ ) is introduced, then we can rewrite the original problem as a coupled system, where u is the solution of the time-fractional diffusion-wave equation and ϕ ˜ = u t ( x , 0 ) . By using the L1 scheme on graded meshes in temporal direction and the compact difference scheme in spatial direction, a fully discrete scheme is constructed for the coupled system. Furthermore, the stability and the local error estimate of the proposed scheme is given. Finally, numerical examples are presented to verify the accuracy and efficiency of the proposed method.
abstractGer	This paper considers the numerical approximation for the time-fractional diffusion-wave equation with the order α ∈ ( 1 , 2 ) , whose solution behaves a weak singularity at t = 0 . To construct the high-order scheme, the intermediate variable w = D t α / 2 ( u − t ϕ ˜ ) is introduced, then we can rewrite the original problem as a coupled system, where u is the solution of the time-fractional diffusion-wave equation and ϕ ˜ = u t ( x , 0 ) . By using the L1 scheme on graded meshes in temporal direction and the compact difference scheme in spatial direction, a fully discrete scheme is constructed for the coupled system. Furthermore, the stability and the local error estimate of the proposed scheme is given. Finally, numerical examples are presented to verify the accuracy and efficiency of the proposed method.
abstract_unstemmed	This paper considers the numerical approximation for the time-fractional diffusion-wave equation with the order α ∈ ( 1 , 2 ) , whose solution behaves a weak singularity at t = 0 . To construct the high-order scheme, the intermediate variable w = D t α / 2 ( u − t ϕ ˜ ) is introduced, then we can rewrite the original problem as a coupled system, where u is the solution of the time-fractional diffusion-wave equation and ϕ ˜ = u t ( x , 0 ) . By using the L1 scheme on graded meshes in temporal direction and the compact difference scheme in spatial direction, a fully discrete scheme is constructed for the coupled system. Furthermore, the stability and the local error estimate of the proposed scheme is given. Finally, numerical examples are presented to verify the accuracy and efficiency of the proposed method.
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title_short	Local error estimates of the fourth-order compact difference scheme for a time-fractional diffusion-wave equation
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up_date	2024-07-06T16:32:09.992Z
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Local error estimates of the fourth-order compact difference scheme for a time-fractional diffusion-wave equation

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