Numerical Method for the Inverse Boundary-Value Problem of the Heat Equation

The article considers the inverse boundary-value problem of heat conduction which involves determining the time distribution of temperature on the boundary given the spatial distribution of the temperature at the final time instant. The problem is reduced to an integral equation of the first kind wi...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Computational mathematics and modeling Jg. 28; H. 2; S. 141 - 147
Hauptverfasser: Dmitriev, V. I., Stolyarov, L. V.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.04.2017
Springer Nature B.V
Schlagworte:
Applications of Mathematics
Boundary value problems
Computational Mathematics and Numerical Analysis
Conduction heating
Conductive heat transfer
I. Inverse Problems
Integral equations
Iterative methods
Mathematical analysis
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Numerical methods
Optimization
Spatial distribution
Thermodynamics
boundary-value problem for the heat equation
method for solving inverse problems
inverse problems
ISSN:1046-283X, 1573-837X
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Abstract The article considers the inverse boundary-value problem of heat conduction which involves determining the time distribution of temperature on the boundary given the spatial distribution of the temperature at the final time instant. The problem is reduced to an integral equation of the first kind with a symmetrical kernel. The integral equation is solved by a special iterative method. Test examples demonstrate convergence and stability of the proposed method.
AbstractList The article considers the inverse boundary-value problem of heat conduction which involves determining the time distribution of temperature on the boundary given the spatial distribution of the temperature at the final time instant. The problem is reduced to an integral equation of the first kind with a symmetrical kernel. The integral equation is solved by a special iterative method. Test examples demonstrate convergence and stability of the proposed method.
Author Stolyarov, L. V.
Dmitriev, V. I.
Author_xml – sequence: 1
  givenname: V. I.
  surname: Dmitriev
  fullname: Dmitriev, V. I.
  email: dmitriev@cs.msu.ru
  organization: Faculty of Computational Mathematics and Cybernetics, Moscow State University
– sequence: 2
  givenname: L. V.
  surname: Stolyarov
  fullname: Stolyarov, L. V.
  organization: Faculty of Computational Mathematics and Cybernetics, Moscow State University
BookMark eNp9kMtOwzAQRS0EEm3hA9hZYm3wo4mdJVSFViqPBaDuLNuxaao0bu0Eib_HbVggJFjNLO6ZuTpDcNz4xgJwQfAVwZhfR4KzQiBMOCpYRhE_AgOScYYE48vjtONxjqhgy1MwjHGNMRaU4QFYPHYbGyqjavhg25UvofMBtisL582HDdHCW981pQqf6E3VnYXPwevabqB3h9TMqhZOd51qK9-cgROn6mjPv-cIvN5NXyYztHi6n09uFshQlgo6Z4gjmrnSmYxqQSjVTo95gYUyJhcZZmXujGWYlFqVSmUu06muzbHVRjE2Apf93W3wu87GVq59F5r0UhIhyLigOeMpxfuUCT7GYJ00VXvo2QZV1ZJguVcne3UyqZN7dXJPkl_kNlSb5OBfhvZMTNnm3YYfnf6EvgArDoNg
CitedBy_id crossref_primary_10_1088_1742_6596_1715_1_012032
crossref_primary_10_3390_a16010033
Cites_doi 10.1016/0041-5553(74)90133-5
10.1007/s10598-012-9117-2
ContentType Journal Article
Copyright Springer Science+Business Media New York 2017
Copyright Springer Science & Business Media 2017
Copyright_xml – notice: Springer Science+Business Media New York 2017
– notice: Copyright Springer Science & Business Media 2017
DBID AAYXX
CITATION
JQ2
DOI 10.1007/s10598-017-9352-7
DatabaseName CrossRef
ProQuest Computer Science Collection
DatabaseTitle CrossRef
ProQuest Computer Science Collection
DatabaseTitleList ProQuest Computer Science Collection
DeliveryMethod fulltext_linktorsrc
Discipline Mathematics
Computer Science
EISSN 1573-837X
EndPage 147
ExternalDocumentID 10_1007_s10598_017_9352_7
GroupedDBID -52
-5D
-5G
-BR
-EM
-Y2
-~C
.86
.DC
.VR
06D
0R~
0VY
1N0
1SB
2.D
28-
29F
2J2
2JN
2JY
2KG
2LR
2P1
2VQ
2~H
30V
4.4
406
408
409
40D
40E
5GY
5QI
5VS
642
67Z
6NX
8TC
8UJ
95-
95.
95~
96X
AAAVM
AABHQ
AACDK
AAHNG
AAIAL
AAJBT
AAJKR
AANZL
AARHV
AARTL
AASML
AATNV
AATVU
AAUYE
AAWCG
AAYIU
AAYQN
AAYTO
AAYZH
ABAKF
ABBBX
ABBXA
ABDZT
ABECU
ABFTV
ABHLI
ABHQN
ABJNI
ABJOX
ABKCH
ABKTR
ABMNI
ABMQK
ABNWP
ABQBU
ABQSL
ABSXP
ABTEG
ABTHY
ABTKH
ABTMW
ABULA
ABWNU
ABXPI
ACAOD
ACBXY
ACDTI
ACGFS
ACHSB
ACHXU
ACIWK
ACKNC
ACMDZ
ACMLO
ACOKC
ACOMO
ACPIV
ACSNA
ACZOJ
ADHHG
ADHIR
ADIMF
ADINQ
ADKNI
ADKPE
ADRFC
ADTPH
ADURQ
ADYFF
ADZKW
AEBTG
AEFIE
AEFQL
AEGAL
AEGNC
AEJHL
AEJRE
AEKMD
AEMSY
AEOHA
AEPYU
AESKC
AETLH
AEVLU
AEXYK
AFBBN
AFEXP
AFGCZ
AFLOW
AFQWF
AFWTZ
AFZKB
AGAYW
AGDGC
AGGDS
AGJBK
AGMZJ
AGQEE
AGQMX
AGRTI
AGWIL
AGWZB
AGYKE
AHAVH
AHBYD
AHKAY
AHSBF
AHYZX
AIAKS
AIGIU
AIIXL
AILAN
AITGF
AJBLW
AJRNO
ALMA_UNASSIGNED_HOLDINGS
ALWAN
AMKLP
AMXSW
AMYLF
AMYQR
AOCGG
ARMRJ
ASPBG
AVWKF
AXYYD
AZFZN
B-.
BA0
BAPOH
BBWZM
BDATZ
BGNMA
BSONS
CAG
COF
CS3
CSCUP
DDRTE
DL5
DNIVK
DPUIP
EBLON
EBS
EIOEI
EJD
ESBYG
FEDTE
FERAY
FFXSO
FIGPU
FINBP
FNLPD
FRRFC
FSGXE
FWDCC
GGCAI
GGRSB
GJIRD
GNWQR
GQ6
GQ7
GQ8
GXS
H13
HF~
HG6
HMJXF
HQYDN
HRMNR
HVGLF
HZ~
IHE
IJ-
IKXTQ
ITM
IWAJR
IXC
IZIGR
IZQ
I~X
I~Z
J-C
JBSCW
JCJTX
JZLTJ
KDC
KOV
KOW
LAK
LLZTM
M4Y
MA-
N2Q
N9A
NB0
NDZJH
NPVJJ
NQJWS
NU0
O9-
O93
O9G
O9I
O9J
OAM
OVD
P19
P2P
P9R
PF0
PT4
PT5
QOK
QOS
R4E
R89
R9I
RHV
RNI
RNS
ROL
RPX
RSV
RZC
RZE
RZK
S16
S1Z
S26
S27
S28
S3B
SAP
SCLPG
SDD
SDH
SDM
SHX
SISQX
SJYHP
SMT
SNE
SNPRN
SNX
SOHCF
SOJ
SPISZ
SRMVM
SSLCW
STPWE
SZN
T13
T16
TEORI
TSG
TSK
TSV
TUC
U2A
UG4
UOJIU
UTJUX
UZXMN
VC2
VFIZW
W23
W48
WK8
XU3
YLTOR
Z83
Z8W
ZMTXR
ZWQNP
~EX
AAPKM
AAYXX
ABDBE
ABFSG
ABJCF
ABRTQ
ACSTC
ADHKG
AEZWR
AFDZB
AFFHD
AFHIU
AFKRA
AFOHR
AGQPQ
AHPBZ
AHWEU
AIXLP
ARAPS
ATHPR
AZQEC
BENPR
BGLVJ
CCPQU
CITATION
DWQXO
GNUQQ
HCIFZ
K7-
M2P
M7S
PHGZM
PHGZT
PQGLB
PTHSS
JQ2
ID FETCH-LOGICAL-c2317-ffc1f1b3fdfc52b8122bfb47908acc68503d6fce301dbadaa5f5b823e60ebca33
IEDL.DBID RSV
ISSN 1046-283X
IngestDate Wed Sep 17 13:41:19 EDT 2025
Tue Nov 18 22:02:20 EST 2025
Sat Nov 29 04:11:53 EST 2025
Fri Feb 21 02:36:27 EST 2025
IsPeerReviewed true
IsScholarly true
Issue 2
Keywords boundary-value problem for the heat equation
method for solving inverse problems
inverse problems
Language English
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c2317-ffc1f1b3fdfc52b8122bfb47908acc68503d6fce301dbadaa5f5b823e60ebca33
Notes ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
PQID 1881492637
PQPubID 2043702
PageCount 7
ParticipantIDs proquest_journals_1881492637
crossref_citationtrail_10_1007_s10598_017_9352_7
crossref_primary_10_1007_s10598_017_9352_7
springer_journals_10_1007_s10598_017_9352_7
PublicationCentury 2000
PublicationDate 20170400
PublicationDateYYYYMMDD 2017-04-01
PublicationDate_xml – month: 4
  year: 2017
  text: 20170400
PublicationDecade 2010
PublicationPlace New York
PublicationPlace_xml – name: New York
PublicationTitle Computational mathematics and modeling
PublicationTitleAbbrev Comput Math Model
PublicationYear 2017
Publisher Springer US
Springer Nature B.V
Publisher_xml – name: Springer US
– name: Springer Nature B.V
References CR2
CR4
CR3
Tikhonov (CR1) 1935; 5
CR5
9352_CR5
9352_CR3
9352_CR4
9352_CR2
AN Tikhonov (9352_CR1) 1935; 5
References_xml – ident: CR3
– ident: CR4
– ident: CR2
– volume: 5
  start-page: 294
  year: 1935
  end-page: 300
  ident: CR1
  article-title: Uniqueness theorem for the heat equation
  publication-title: Dokl. Akad. Nauk
– ident: CR5
– ident: 9352_CR3
  doi: 10.1016/0041-5553(74)90133-5
– ident: 9352_CR5
  doi: 10.1007/s10598-012-9117-2
– ident: 9352_CR4
– volume: 5
  start-page: 294
  year: 1935
  ident: 9352_CR1
  publication-title: Dokl. Akad. Nauk
– ident: 9352_CR2
SSID ssj0008230
Score 2.0062797
Snippet The article considers the inverse boundary-value problem of heat conduction which involves determining the time distribution of temperature on the boundary...
SourceID proquest
crossref
springer
SourceType Aggregation Database
Enrichment Source
Index Database
Publisher
StartPage 141
SubjectTerms Applications of Mathematics
Boundary value problems
Computational Mathematics and Numerical Analysis
Conduction heating
Conductive heat transfer
I. Inverse Problems
Integral equations
Iterative methods
Mathematical analysis
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Numerical methods
Optimization
Spatial distribution
Thermodynamics
Title Numerical Method for the Inverse Boundary-Value Problem of the Heat Equation
URI https://link.springer.com/article/10.1007/s10598-017-9352-7
https://www.proquest.com/docview/1881492637
Volume 28
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
journalDatabaseRights – providerCode: PRVAVX
  databaseName: SpringerLink
  customDbUrl:
  eissn: 1573-837X
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0008230
  issn: 1046-283X
  databaseCode: RSV
  dateStart: 19970101
  isFulltext: true
  titleUrlDefault: https://link.springer.com/search?facet-content-type=%22Journal%22
  providerName: Springer Nature
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1LSwMxEB60etCD1apYrZKDJyWwj2Z3c1Rp6cGWglp6W_IEobS62wr-e5PsbltFBT1nNoSZZGaWmfk-gEsZEy6lDjGVguA25RwzFmpMqYhZoo3PpMKRTcSDQTIe02E5x51X3e5VSdJ56rVhN2LHwYxXpSZrwPEmbBELNmN_0R9GS_drK0cFBEGETewcV6XM77b4HIxWGeaXoqiLNd36v065D3tlaoluirtwABtq2oB6RduAylfcgN3-Eqo1P4T7waIo2kxQ37FJI5PGIiOALARHlit065iXsnc8YpOFQsOCggbNtJPqGWeOOq8FYvgRPHU7j3c9XFIsYGESuxhrLXzt81BLLUjATbQPuObtmHoJEyJKiBfKSAtl3IDkTDJGNOFGwyrybBdVGB5DbTqbqhNASigpPMmoRZyhirCEaZPeeDKWOmqLoAlepetUlPjjlgZjkq6Qk63uUqO71OoujZtwtfzkpQDf-E24VRkwLd9hnvpJ4ltIxNAsX1cGW1v-abPTP0mfwU5gLe4aelpQm2cLdQ7b4m3-nGcX7np-AE4M4Cw
linkProvider Springer Nature
linkToHtml http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1LSwMxEB60CurBalWsVs3BkxLY926OKi0V21Kwlt6WPEEore62gv_eZB9tFRX0nNkQZpKZWWbm-wAuRegzIZSLieA-9ghjmFJXYUJ4SCOlfSbhGdlE2OtFoxHpF3PcadntXpYkM0-9Muzmm3Ew7VWJzhpwuA4bnmHZMb_oj8OF-zWVoxyCIMA6do7KUuZ3W3wORssM80tRNIs1req_TrkHu0VqiW7yu7APa3JSg2pJ24CKV1yDne4CqjU9gE5vnhdtxqibsUkjncYiLYAMBEeSSnSbMS8l73hIx3OJ-jkFDZqqTKqtnTlqvuaI4Yfw1GoO7tq4oFjAXCd2IVaK28pmrhKK-w7T0d5hinkhsSLKeRD5lisCxaV2A4JRQamvfKY1LAPLdFG57hFUJtOJPAYkuRTcEpQYxBkifRpRpdMbS4RCBR536mCVuo55gT9uaDDG8RI52egu1rqLje7isA5Xi09ecvCN34QbpQHj4h2msR1FtoFEdPXydWmwleWfNjv5k_QFbLUH3U7cue89nMK2Y6yfNfc0oDJL5vIMNvnb7DlNzrOr-gHYueMQ
linkToPdf http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LTwIxEJ4oGqMHUdSIovbgSdOwsOyjRx8QjLAhPgi3TZ-JCQHcBRP_ve0-AI2aGM-dbZppO_02M_N9AOfCc5gQysZEcAc3CGOYUlthQrhHfaVjJuGJ2IQXBP5gQHqZzmmcV7vnKcm0p8GwNI2m1YlQ1aXGN8e0hukISzSCwN4qrDX0j4yp6Xp47M9DsckipXQELtbv6CBPa343xeeHaYE2vyRIk3enVfz3indgO4Oc6Co9I7uwIkclKOZyDii73SXY6s4pXOM96ASzNJkzRN1EZRppeIu0ATLUHFEs0XWiyBS94z4dziTqpdI0aKwSq7YO8qj5mjKJ78Nzq_l008aZ9ALmGvB5WCleUzVmK6G4U2caBdSZYg2PWD7l3PUdyxau4lKHB8GooNRRDtPelq5lqqts-wAKo_FIHgKSXApuCUoMEw2RDvWp0rDHEp5QboPXy2Dlfg95xktu5DGG4YJR2fgu1L4Lje9CrwwX808mKSnHb8aVfDPD7H7GYc33a4Yq0dbDl_nmLQ3_NNnRn6zPYKN32wo7d8H9MWzWzeYnNT8VKEyjmTyBdf42fYmj0-TUfgB2huv0
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Numerical+Method+for+the+Inverse+Boundary-Value+Problem+of+the+Heat+Equation&rft.jtitle=Computational+mathematics+and+modeling&rft.au=Dmitriev%2C+V.+I.&rft.au=Stolyarov%2C+L.+V.&rft.date=2017-04-01&rft.issn=1046-283X&rft.eissn=1573-837X&rft.volume=28&rft.issue=2&rft.spage=141&rft.epage=147&rft_id=info:doi/10.1007%2Fs10598-017-9352-7&rft.externalDBID=n%2Fa&rft.externalDocID=10_1007_s10598_017_9352_7
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1046-283X&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1046-283X&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1046-283X&client=summon