Homotopy Perturbation Method

Homotopy perturbation method (HPM) is a semi‐analytical technique for solving linear as well as nonlinear ordinary/partial differential equations. The method may also be used to solve a system of coupled linear and nonlinear differential equations. This chapter first illustrates the basic...

Celý popis

Uložené v:
Podrobná bibliografia
Vydané v:Advanced Numerical and Semi-Analytical Methods for Differential Equations s. 131 - 139
Hlavní autori: Chakraverty, Snehashish, Mahato, Nisha, Karunakar, Perumandla, Dilleswar Rao, Tharasi
Médium: Kapitola
Jazyk:English
Vydavateľské údaje: United States Wiley 2019
John Wiley & Sons, Incorporated
John Wiley & Sons, Inc
Vydanie:1
Predmet:
coupled differential equations
homotopy perturbation method
nonlinear ordinary differential equation
nonlinear partial differential equation
Art
Perturbation methods
IEEE Sections
Ear
Boundary conditions
Strain
Convergence
ISBN:9781119423423, 1119423422
On-line prístup:Získať plný text
Tagy: Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
Abstract Homotopy perturbation method (HPM) is a semi‐analytical technique for solving linear as well as nonlinear ordinary/partial differential equations. The method may also be used to solve a system of coupled linear and nonlinear differential equations. This chapter first illustrates the basic idea of the HPM. It uses the present method to solve a nonlinear ordinary differential equation, a nonlinear partial differential equation, and a coupled nonlinear system of partial differential equations. It is worth mentioning that the HPM can also be used for handling linear ordinary and partial differential equations. The test problems demonstrated in the chapter confirm that the HPM is an efficient method for solving linear/nonlinear ordinary, partial, and coupled differential equations. The series usually converges with an increase in the number of terms, but one may not expect the compact form solution always.
AbstractList Homotopy perturbation method (HPM) is a semi‐analytical technique for solving linear as well as nonlinear ordinary/partial differential equations. The method may also be used to solve a system of coupled linear and nonlinear differential equations. This chapter first illustrates the basic idea of the HPM. It uses the present method to solve a nonlinear ordinary differential equation, a nonlinear partial differential equation, and a coupled nonlinear system of partial differential equations. It is worth mentioning that the HPM can also be used for handling linear ordinary and partial differential equations. The test problems demonstrated in the chapter confirm that the HPM is an efficient method for solving linear/nonlinear ordinary, partial, and coupled differential equations. The series usually converges with an increase in the number of terms, but one may not expect the compact form solution always.
Homotopy perturbation method (HPM) is a semi‐analytical technique for solving linear as well as nonlinear ordinary/partial differential equations. The method may also be used to solve a system of coupled linear and nonlinear differential equations. This chapter first illustrates the basic idea of the HPM. It uses the present method to solve a nonlinear ordinary differential equation, a nonlinear partial differential equation, and a coupled nonlinear system of partial differential equations. It is worth mentioning that the HPM can also be used for handling linear ordinary and partial differential equations. The test problems demonstrated in the chapter confirm that the HPM is an efficient method for solving linear/nonlinear ordinary, partial, and coupled differential equations. The series usually converges with an increase in the number of terms, but one may not expect the compact form solution always.
Author Karunakar, Perumandla
Dilleswar Rao, Tharasi
Mahato, Nisha
Chakraverty, Snehashish
Author_xml – sequence: 1
  givenname: Snehashish
  surname: Chakraverty
  fullname: Chakraverty, Snehashish
– sequence: 2
  givenname: Nisha
  surname: Mahato
  fullname: Mahato, Nisha
– sequence: 3
  givenname: Perumandla
  surname: Karunakar
  fullname: Karunakar, Perumandla
– sequence: 4
  givenname: Tharasi
  surname: Dilleswar Rao
  fullname: Dilleswar Rao, Tharasi
BookMark eNpVj8tOwzAQRY14CFr6ASAW_YGUGduJPUtUAUUqggWsLcedqhElLokr1L8nJSzoZkZzpXNHZyBO6lizENcIEwSQt2QsIpKWShc4CSuUR2L0L1RwfHBLdSYGCARGWjDqXIzatipBGbCUG7oQN7P4GVPc7Mav3KRtU_pUxXr8zGkVF5fidOnXLY_-9lC8P9y_TWfZ_OXxaXo3zyrsirMceUneQAiSrSLjC1sE0ho9LdAGpRBwYb1easjJe4vGGwq5VYZNyUGroVB973e15p3jMsaP1iG4vbM7cHZ759_RUbqnNk382nKbejBwnRq_Diu_Sdy0LjcapdRdl3GoqcOueqxiZte_soUlJUH9AD3aYa0
ContentType Book Chapter
Copyright 2019 Wiley
2019 John Wiley & Sons, Inc.
Copyright_xml – notice: 2019 Wiley
– notice: 2019 John Wiley & Sons, Inc.
DBID FFUUA
DOI 10.1002/9781119423461.ch12
DatabaseName ProQuest Ebook Central - Book Chapters - Demo use only
DatabaseTitleList

DeliveryMethod fulltext_linktorsrc
Discipline Mathematics
EISBN 9781119423430
9781119423447
9781119423461
1119423449
1119423430
1119423465
Edition 1
EndPage 139
ExternalDocumentID 10.1002/9781119423461.ch12
EBC5741224_107_149
8689320
Genre chapter
GroupedDBID 38.
3XM
AABBV
ABARN
ABQPQ
ADUVA
ADVEM
AERYV
AFOJC
AFPKT
AJFER
AK3
AKQZE
ALMA_UNASSIGNED_HOLDINGS
AUUOE
AZZ
BBABE
BEFXN
BFFAM
BGNUA
BKEBE
BPEOZ
CZZ
ECNEQ
ERSLE
GEOUK
GQOVZ
IETMW
IPJKO
IVUIE
JFSCD
KKBTI
LMJTD
LQKAK
LWYJN
LYPXV
MRDEW
OCL
OHILO
OODEK
W1A
YPLAZ
ZEEST
ABAZT
ABBFG
ACGYG
ACLGV
ACNUM
AENVZ
AHWGJ
FFUUA
WIIVT
ID FETCH-LOGICAL-i1072-51ef9a70cc2e8397a686c9441a9d18c33101d8a4f4059aa817a79c5837e7bec43
ISBN 9781119423423
1119423422
IngestDate Sat Nov 15 22:28:24 EST 2025
Tue Oct 21 07:34:01 EDT 2025
Fri Nov 11 10:38:51 EST 2022
IsPeerReviewed false
IsScholarly false
Keywords Art
Perturbation methods
IEEE Sections
Ear
Boundary conditions
Strain
Convergence
LCCallNum QA371 .C435 2019
Language English
LinkModel OpenURL
MergedId FETCHMERGED-LOGICAL-i1072-51ef9a70cc2e8397a686c9441a9d18c33101d8a4f4059aa817a79c5837e7bec43
OCLC 1090728073
PQID EBC5741224_107_149
PageCount 9
ParticipantIDs proquest_ebookcentralchapters_5741224_107_149
ieee_books_8689320
wiley_ebooks_10_1002_9781119423461_ch12_ch12
PublicationCentury 2000
PublicationDate 2019
2019-04-30
PublicationDateYYYYMMDD 2019-01-01
2019-04-30
PublicationDate_xml – year: 2019
  text: 2019
PublicationDecade 2010
PublicationPlace United States
PublicationPlace_xml – name: United States
– name: Hoboken, NJ, USA
PublicationTitle Advanced Numerical and Semi-Analytical Methods for Differential Equations
PublicationYear 2019
Publisher Wiley
John Wiley & Sons, Incorporated
John Wiley & Sons, Inc
Publisher_xml – name: Wiley
– name: John Wiley & Sons, Incorporated
– name: John Wiley & Sons, Inc
References Wazwaz (c12-cit-0010) 2010
He (c12-cit-0009) 1999; 34
Liu (c12-cit-0002) 1997
Karunakar, Chakraverty (c12-cit-0004) 2018; 35
Liao (c12-cit-0007) 1995; 30
Karunakar, Chakraverty (c12-cit-0003) 2017; 27
Liao (c12-cit-0008) 1997; 20
He (c12-cit-0006) 2004; 151
He (c12-cit-0001) 1999; 178
He (c12-cit-0005) 2003; 135
Sweilam, Khader (c12-cit-0011) 2009; 58
References_xml – volume: 135
  start-page: 73
  issue: 1
  year: 2003
  end-page: 79
  ident: c12-cit-0005
  article-title: Homotopy perturbation method: a new nonlinear analytical technique
  publication-title: Applied Mathematics and Computation
– volume: 151
  start-page: 287
  issue: 1
  year: 2004
  end-page: 292
  ident: c12-cit-0006
  article-title: The homotopy perturbation method for nonlinear oscillators with discontinuities
  publication-title: Applied Mathematics and Computation
– start-page: 47
  year: 1997
  end-page: 53
  ident: c12-cit-0002
  article-title: New research directions in singular perturbation theory: artificial parameter approach and inverse‐perturbation technique
– volume: 35
  start-page: 1610
  issue: 4
  year: 2018
  end-page: 1624
  ident: c12-cit-0004
  article-title: Solution of interval shallow water wave equations using homotopy perturbation method
  publication-title: Engineering Computations
– volume: 30
  start-page: 371
  issue: 3
  year: 1995
  end-page: 380
  ident: c12-cit-0007
  article-title: An approximate solution technique not depending on small parameters: a special example
  publication-title: International Journal of Non‐Linear Mechanics
– volume: 27
  start-page: 2015
  issue: 9
  year: 2017
  end-page: 2029
  ident: c12-cit-0003
  article-title: Comparison of solutions of linear and non‐linear shallow water wave equations using homotopy perturbation method
  publication-title: International Journal of Numerical Methods for Heat and Fluid Flow
– volume: 58
  start-page: 2134
  issue: 11
  year: 2009
  end-page: 2141
  ident: c12-cit-0011
  article-title: Exact solutions of some coupled nonlinear partial differential equations using the homotopy perturbation method
  publication-title: Computers and Mathematics with Applications
– volume: 178
  start-page: 257
  issue: 3
  year: 1999
  end-page: 262
  ident: c12-cit-0001
  article-title: Homotopy perturbation technique
  publication-title: Computer Methods in Applied Mechanics and Engineering
– volume: 34
  start-page: 699
  issue: 4
  year: 1999
  end-page: 708
  ident: c12-cit-0009
  article-title: Variational iteration method–a kind of non‐linear analytical technique: some examples
  publication-title: International Journal of Non‐Linear Mechanics
– volume: 20
  start-page: 91
  issue: 2
  year: 1997
  end-page: 99
  ident: c12-cit-0008
  article-title: Boundary element method for general nonlinear differential operators
  publication-title: Engineering Analysis with Boundary Elements
– year: 2010
  ident: c12-cit-0010
  article-title: Partial Differential Equations and Solitary Waves Theory
SSID ssib037089579
ssj0002152863
ssib035724529
ssib043664869
ssib050313482
Score 1.561394
Snippet Homotopy perturbation method (HPM) is a semi‐analytical technique for solving linear as well as nonlinear ordinary/partial differential equations. The...
Homotopy perturbation method (HPM) is a semi‐analytical technique for solving linear as well as nonlinear ordinary/partial differential equations. The method...
SourceID wiley
proquest
ieee
SourceType Publisher
StartPage 131
SubjectTerms coupled differential equations
homotopy perturbation method
nonlinear ordinary differential equation
nonlinear partial differential equation
Title Homotopy Perturbation Method
URI http://ieeexplore.ieee.org/xpl/articleDetails.jsp?reload=true&arnumber=8689320
http://ebookcentral.proquest.com/lib/SITE_ID/reader.action?docID=5741224&ppg=149&c=UERG
https://onlinelibrary.wiley.com/doi/abs/10.1002/9781119423461.ch12
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV3Pb9MwFLa6wQG4MH6IjoF6YCcwLE4a21dGx6RpZYJN2i3yHFupGGmXtNv4Z_hbefZz06TjsgMXq4rcyPazX957_t77CHlnuY3tUFoKjpeiCc81FcZElLmPcWLEkFkkm-DjsTg_lye93p9lLsz1JS9LcXsrZ_9V1PAMhO1SZ-8h7ual8AB-g9ChBbFDu2YRd2OviDleXumPF3gVg5UAfphfE-rrj2Do-tjzRvtSDKD0kCJl7mLno6tFK4TnDFyXK1jfqOr9dzVFRJGqVD1ZRbIL5ZmYYE_VRaPjj1S1KNVPRG-fmMpdFeSXK1SQBxM4KmiEmpWmcKROddHewYcOKDid_Xb_hw_jBW5VHHo7WOHyozrBin-ggYIqDGWbm4Qu9G9BEUuw9xJMSb6j7bF6bKtfGn3URYBld0prR1gXda209ujz_hAsKrBiMvCCwQuSu_HB7Io6TjJ3d78bf8H9sUE2OAct-uDr6NvZURPDc5zAIo09AVUYKAtlxJqBh0Qt6Pzp7kADpU_Hu2n7SN7IOX1KnrjEl4HLSIHhb5GeKZ-Rx8dNXd_6OdlZymTQlskAZfKCnB2MTvcPaeDXoBOYLqPDyFip-J7WzMDR5CoVqZZgHyuZR0LHYPlHuVCJBaNeKiUirrjUQxFzw-HoJ_FLsllOS_OKDHSaaxkl6kJZnWiWSmZFLlIrHHKVibxPttxEM3cw6kykYCWzvT6hy2lnHhoQ8Mga51lna8Lpkw9-bbBznWHFbZZ11jVz6-qb7Xu-_jV5tNqyO2RzXi3MG_JQX88ndfU2yP4vLrh-vw
linkProvider ProQuest Ebooks
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%3Abook&rft.genre=bookitem&rft.title=Advanced+Numerical+and+Semi-Analytical+Methods+for+Differential+Equations&rft.au=Dilleswar+Rao%2C+Tharasi&rft.au=Mahato%2C+Nisha&rft.au=Karunakar%2C+Perumandla&rft.au=Chakraverty%2C+Snehashish&rft.atitle=Homotopy+Perturbation+Method&rft.date=2019-01-01&rft.pub=John+Wiley+%26+Sons%2C+Incorporated&rft.isbn=9781119423423&rft_id=info:doi/10.1002%2F9781119423461.ch12&rft.externalDBID=149&rft.externalDocID=EBC5741224_107_149
thumbnail_s http://cvtisr.summon.serialssolutions.com/2.0.0/image/custom?url=https%3A%2F%2Febookcentral.proquest.com%2Fcovers%2F5741224-l.jpg