Solution of delay differential equations via a homotopy perturbation method

Delay differential equations (denoted as DDE) have a wide range of application in science and engineering. They arise when the rate of change of a time-dependent process in its mathematical modeling is not only determined by its present state but also by a certain past state. Recent studies in such...

Full description

Saved in:

Bibliographic Details
Published in:	Mathematical and computer modelling Vol. 48; no. 3; pp. 486 - 498
Main Authors:	Shakeri, Fatemeh, Dehghan, Mehdi
Format:	Journal Article
Language:	English
Published:	Oxford Elsevier Ltd 01.08.2008 Elsevier Science
Subjects:	Applications in mathematical biology and engineering Delay differential equations Exact sciences and technology Homotopy perturbation method Mathematical analysis Mathematics Methods of scientific computing (including symbolic computation, algebraic computation) Numerical analysis Numerical analysis. Scientific computation Ordinary differential equations Sciences and techniques of general use Delay differential equations Homotopy perturbation method Applications in mathematical biology and engineering Differential equation Numerical method Delay equation Perturbation method Numerical analysis Scientific computation Applied mathematics Homotopy Mathematical model Computer aided analysis
ISSN:	0895-7177, 1872-9479
Online Access:	Get full text
Tags:	Add Tag No Tags, Be the first to tag this record!

Abstract	Delay differential equations (denoted as DDE) have a wide range of application in science and engineering. They arise when the rate of change of a time-dependent process in its mathematical modeling is not only determined by its present state but also by a certain past state. Recent studies in such diverse fields as biology, economy, control and electrodynamics have shown that DDEs play an important role in explaining many different phenomena. In particular they turn out to be fundamental when ODE-based models fail. In this research, the solution of a delay differential equation is presented by means of a homotopy perturbation method and then some numerical illustrations are given. These results reveal that the proposed method is very effective and simple to perform.
AbstractList	Delay differential equations (denoted as DDE) have a wide range of application in science and engineering. They arise when the rate of change of a time-dependent process in its mathematical modeling is not only determined by its present state but also by a certain past state. Recent studies in such diverse fields as biology, economy, control and electrodynamics have shown that DDEs play an important role in explaining many different phenomena. In particular they turn out to be fundamental when ODE-based models fail. In this research, the solution of a delay differential equation is presented by means of a homotopy perturbation method and then some numerical illustrations are given. These results reveal that the proposed method is very effective and simple to perform.
Author	Dehghan, Mehdi Shakeri, Fatemeh
Author_xml	– sequence: 1 givenname: Fatemeh surname: Shakeri fullname: Shakeri, Fatemeh email: fatemehshakeri@aut.ac.ir – sequence: 2 givenname: Mehdi surname: Dehghan fullname: Dehghan, Mehdi email: mdehghan@aut.ac.ir
BackLink	http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=20470560$$DView record in Pascal Francis
BookMark	eNp9kEtPwzAQhC1UJMrjB3DzhWPCOq7jRJxQxUsgcQDO1saxVVdJXGy3Uv89aQsXDj2NtDPfanfOyWTwgyHkmkHOgJW3y7zXfV4AyBzqfJyckCmrZJHVM1lPyBSqWmSSSXlGzmNcAoCooZqS1w_frZPzA_WWtqbDLW2dtSaYITnsqPle486OdOOQIl343ie_2tKVCWkdmr1Je5MWvr0kpxa7aK5-9YJ8PT58zp-zt_enl_n9W6Z5IVMmha4NL7m12BSiERJF2XBWac15g7a0VlQcbcWZsaKcQTtKq6HEssAZSuQX5Oawd4VRY2cDDtpFtQqux7BVBcwkiBLGnDzkdPAxBmOVdml_cAroOsVA7bpTSzV2p3bdKajVOBlJ9o_8W36MuTswZnx940xQUTszaNO6YHRSrXdH6B-eCYsP
CitedBy_id	crossref_primary_10_1108_HFF_09_2011_0192 crossref_primary_10_1016_j_cnsns_2011_07_018 crossref_primary_10_1002_cnm_1399 crossref_primary_10_1002_cnm_1398 crossref_primary_10_1063_5_0271644 crossref_primary_10_1002_mma_2676 crossref_primary_10_1007_s00366_021_01422_7 crossref_primary_10_1016_j_asoc_2014_08_055 crossref_primary_10_1007_s11075_016_0188_6 crossref_primary_10_1108_09615531111105399 crossref_primary_10_1007_s40314_019_0953_y crossref_primary_10_1016_j_cnsns_2012_05_009 crossref_primary_10_1155_2008_956170 crossref_primary_10_1088_0253_6102_53_6_02 crossref_primary_10_1016_j_jksus_2011_08_005 crossref_primary_10_1016_j_mcm_2010_04_007 crossref_primary_10_1155_2010_561364 crossref_primary_10_1007_s40995_017_0467_7 crossref_primary_10_1108_EC_02_2022_0094 crossref_primary_10_1108_09615531211231235 crossref_primary_10_1007_s40819_015_0072_4 crossref_primary_10_1016_j_camwa_2009_03_017 crossref_primary_10_1016_j_cpc_2009_01_012 crossref_primary_10_1108_09615531211244934 crossref_primary_10_1007_s11075_011_9448_7 crossref_primary_10_1002_num_20490 crossref_primary_10_1108_09615531211215792 crossref_primary_10_1002_cnm_1200 crossref_primary_10_1002_cnm_1288 crossref_primary_10_1007_s11760_015_0811_3 crossref_primary_10_1088_0031_8949_78_06_065004 crossref_primary_10_1080_00207160802247646 crossref_primary_10_3390_sym13030418 crossref_primary_10_1007_s00366_021_01491_8 crossref_primary_10_1016_j_cam_2016_02_025 crossref_primary_10_1016_j_apm_2023_02_018 crossref_primary_10_1140_epjp_i2017_11344_9 crossref_primary_10_1155_2022_9512048 crossref_primary_10_1002_num_20413 crossref_primary_10_1016_j_advwatres_2009_09_003 crossref_primary_10_1002_num_20416 crossref_primary_10_1088_1742_6596_1730_1_012114 crossref_primary_10_1088_1742_6596_890_1_012023 crossref_primary_10_1515_phys_2015_0052 crossref_primary_10_1016_j_molliq_2013_09_010 crossref_primary_10_1186_s13662_021_03340_w crossref_primary_10_1002_mma_1329 crossref_primary_10_1080_00207160902783540 crossref_primary_10_1016_j_jksus_2010_07_016 crossref_primary_10_1080_02286203_2024_2315534 crossref_primary_10_1007_s11071_019_05403_w crossref_primary_10_1007_s00366_020_01219_0 crossref_primary_10_1016_j_cpc_2010_02_018 crossref_primary_10_1002_mma_1601 crossref_primary_10_1016_j_aml_2011_03_032 crossref_primary_10_1080_00207160_2010_488292 crossref_primary_10_1155_2017_7269450 crossref_primary_10_1007_s40324_017_0117_1 crossref_primary_10_1186_s13662_018_1717_5 crossref_primary_10_1007_s40819_017_0374_9 crossref_primary_10_1007_s40819_022_01466_3 crossref_primary_10_1163_156939312798954964 crossref_primary_10_1016_j_apm_2015_01_001 crossref_primary_10_1002_mma_9178 crossref_primary_10_1002_mma_2890 crossref_primary_10_1002_mma_8358 crossref_primary_10_1016_j_jocs_2023_102206 crossref_primary_10_1177_1461348419830210 crossref_primary_10_1002_fld_2211 crossref_primary_10_1016_j_jksus_2010_04_008 crossref_primary_10_1080_00207160_2017_1344230 crossref_primary_10_1002_mma_4839 crossref_primary_10_1002_mma_2647 crossref_primary_10_1002_mma_2801 crossref_primary_10_1016_j_cpc_2010_02_007 crossref_primary_10_1108_09615531211244916 crossref_primary_10_1155_2008_869614 crossref_primary_10_1007_s42452_018_0130_8 crossref_primary_10_1155_2015_273830 crossref_primary_10_1155_2015_382475 crossref_primary_10_1177_1077546312464988 crossref_primary_10_1016_j_apm_2014_09_003 crossref_primary_10_1016_j_chaos_2023_113481 crossref_primary_10_1002_mma_7020 crossref_primary_10_1140_epjp_i2017_11512_y crossref_primary_10_1016_j_mcm_2011_09_037 crossref_primary_10_1186_s13662_019_1961_3 crossref_primary_10_1371_journal_pcbi_1008633 crossref_primary_10_1108_09615531111123119 crossref_primary_10_1016_j_amc_2020_125334 crossref_primary_10_1007_s40819_016_0212_5 crossref_primary_10_3390_math7060532 crossref_primary_10_1016_j_physleta_2009_07_002 crossref_primary_10_1016_j_apm_2012_02_041 crossref_primary_10_1002_cnm_1352 crossref_primary_10_1016_j_cam_2013_08_018 crossref_primary_10_1080_00207160903023581 crossref_primary_10_1007_s40819_017_0390_9 crossref_primary_10_1016_j_cnsns_2012_01_032 crossref_primary_10_1007_s40995_023_01445_3 crossref_primary_10_1080_00207160903019480 crossref_primary_10_1108_09615531311301245 crossref_primary_10_1080_00207160903477159 crossref_primary_10_1177_1077546311408467 crossref_primary_10_1016_j_amc_2014_03_090 crossref_primary_10_1080_00207160902874653 crossref_primary_10_1016_j_cam_2015_06_005 crossref_primary_10_1002_apj_647 crossref_primary_10_1016_j_cnsns_2011_03_039 crossref_primary_10_1108_09615531111162783 crossref_primary_10_1002_fld_2315 crossref_primary_10_1016_j_tsep_2024_102563 crossref_primary_10_3390_mca27050081 crossref_primary_10_1002_nme_3122 crossref_primary_10_1002_num_20441 crossref_primary_10_1108_09615531211199854 crossref_primary_10_1016_j_amc_2011_11_082 crossref_primary_10_1002_num_20565 crossref_primary_10_1080_09720502_2020_1850994 crossref_primary_10_1108_09615531011081423 crossref_primary_10_1002_mma_3556 crossref_primary_10_1080_00207160903082389 crossref_primary_10_1108_09615531011056809 crossref_primary_10_1002_mma_3277 crossref_primary_10_1016_j_apm_2011_12_020 crossref_primary_10_1016_j_jksus_2010_07_007 crossref_primary_10_1016_j_jksus_2017_09_019 crossref_primary_10_1016_j_amc_2012_09_048 crossref_primary_10_1016_j_physa_2017_12_007 crossref_primary_10_1155_2022_1049561 crossref_primary_10_1016_j_apm_2012_09_032 crossref_primary_10_1007_s10440_008_9318_z crossref_primary_10_1038_s41598_023_33461_z crossref_primary_10_1080_00207160903128497 crossref_primary_10_1155_2014_937345 crossref_primary_10_1155_2022_3218213 crossref_primary_10_1080_09720502_2019_1694742 crossref_primary_10_1155_2013_939143 crossref_primary_10_1016_j_apnum_2016_12_003 crossref_primary_10_1007_s10778_018_0864_4 crossref_primary_10_1016_j_cap_2010_03_015 crossref_primary_10_1016_j_icheatmasstransfer_2010_03_009 crossref_primary_10_1016_j_jksus_2010_05_008 crossref_primary_10_1016_j_cnsns_2016_12_027 crossref_primary_10_1002_mma_1246 crossref_primary_10_1108_09615531011016957 crossref_primary_10_1155_2014_631416 crossref_primary_10_32604_cmc_2022_030888 crossref_primary_10_1016_j_jksus_2010_05_005 crossref_primary_10_1016_j_cam_2012_11_013 crossref_primary_10_1155_2016_6862028 crossref_primary_10_1016_j_chaos_2009_03_147 crossref_primary_10_1016_j_apm_2011_09_082 crossref_primary_10_1063_5_0195270 crossref_primary_10_1080_00207160802545908 crossref_primary_10_1007_s11063_017_9711_6 crossref_primary_10_1108_HFF_03_2011_0070 crossref_primary_10_1155_2022_7519002 crossref_primary_10_1002_num_20460 crossref_primary_10_1155_2020_7359242 crossref_primary_10_1016_j_camwa_2012_03_053 crossref_primary_10_1155_2013_498902 crossref_primary_10_1186_1687_1847_2012_178 crossref_primary_10_1515_IJNSNS_2009_10_2_235 crossref_primary_10_1016_j_apnum_2020_07_001 crossref_primary_10_1002_cnm_1146 crossref_primary_10_1051_matecconf_201712502001 crossref_primary_10_1002_mma_1599 crossref_primary_10_1002_mma_10043 crossref_primary_10_1016_j_apnum_2013_11_003 crossref_primary_10_1002_cnm_1308 crossref_primary_10_1016_j_camwa_2008_11_003 crossref_primary_10_1016_j_proeng_2012_06_319 crossref_primary_10_1007_s40995_019_00812_3 crossref_primary_10_1016_j_apm_2016_02_005 crossref_primary_10_1155_2022_8130940 crossref_primary_10_1016_j_amc_2015_06_012 crossref_primary_10_1016_j_jksuci_2023_101890 crossref_primary_10_1007_s10915_024_02696_x crossref_primary_10_1002_num_20473 crossref_primary_10_1080_10236198_2016_1142539 crossref_primary_10_1016_j_apnum_2021_05_024 crossref_primary_10_1140_epjp_i2018_11859_5 crossref_primary_10_1002_num_20478 crossref_primary_10_1002_num_20511
Cites_doi	10.1016/j.cam.2006.07.030 10.1016/j.physleta.2006.03.039 10.1088/0031-8949/75/6/007 10.2528/PIER07090403 10.1016/j.chaos.2006.04.019 10.1016/S0045-7825(99)00018-3 10.1016/j.physleta.2005.10.005 10.1016/j.physleta.2006.11.062 10.1016/j.chaos.2005.08.180 10.1016/j.amc.2006.10.001 10.1088/0031-8949/75/4/031 10.1016/j.matcom.2005.10.001 10.1615/JPorMedia.v11.i8.50 10.1002/num.20071 10.1016/S0096-3003(01)00312-5 10.1016/j.chaos.2006.06.037 10.1016/j.chaos.2005.03.006 10.1002/cnm.832 10.1016/S0020-7462(98)00085-7 10.1016/j.chaos.2006.09.070 10.1016/j.amc.2006.09.019 10.1016/j.chaos.2006.05.074
ContentType	Journal Article
Copyright	2007 Elsevier Ltd 2008 INIST-CNRS
Copyright_xml	– notice: 2007 Elsevier Ltd – notice: 2008 INIST-CNRS
DBID	6I. AAFTH AAYXX CITATION IQODW
DOI	10.1016/j.mcm.2007.09.016
DatabaseName	ScienceDirect Open Access Titles Elsevier:ScienceDirect:Open Access CrossRef Pascal-Francis
DatabaseTitle	CrossRef
DatabaseTitleList
DeliveryMethod	fulltext_linktorsrc
Discipline	Engineering Mathematics
EISSN	1872-9479
EndPage	498
ExternalDocumentID	20470560 10_1016_j_mcm_2007_09_016 S0895717707003342
GroupedDBID	--K --M -DZ -~X .DC .~1 0R~ 0SF 186 1B1 1RT 1~. 1~5 29M 4.4 4G. 5GY 5VS 6I. 7-5 71M 8P~ 9JN 9JO AACTN AAEDT AAEDW AAFTH AAIKJ AAKOC AALRI AAOAW AAQFI AAQXK AARIN AAXUO ABAOU ABFNM ABMAC ABUCO ABVKL ABXDB ABYKQ ACAZW ACDAQ ACGFS ACNNM ACRLP ADBBV ADEZE ADMUD ADTZH AEBSH AECPX AEKER AEXQZ AFFNX AFKWA AFTJW AGHFR AGUBO AGYEJ AHHHB AHJVU AIEXJ AIGVJ AIKHN AITUG AJBFU AJOXV ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ ASPBG AVWKF AXJTR AZFZN BKOJK BLXMC CS3 DU5 EBS EFJIC EFLBG EJD EO8 EO9 EP2 EP3 F5P FDB FEDTE FGOYB FIRID FNPLU FYGXN G-2 G-Q HAMUX HVGLF HZ~ IHE IXB J1W JJJVA KOM LG9 M26 M41 MHUIS MO0 MVM N9A NCXOZ O-L O9- OAUVE OK1 OZT P-8 P-9 P2P PC. Q38 R2- RIG RNS ROL RPZ SDF SDG SES SEW SPC SSB SSD SST SSW SSZ T5K T9H TN5 VOH WUQ XPP XSW YNT YQT ZMT 9DU AATTM AAXKI AAYWO AAYXX ABJNI ABWVN ACLOT ACRPL ACVFH ADCNI ADNMO ADVLN AEIPS AEUPX AFPUW AGQPQ AIGII AIIUN AKBMS AKRWK AKYEP ANKPU CITATION EFKBS ~HD AFXIZ AGCQF AGRNS IQODW SSH
ID	FETCH-LOGICAL-c327t-75c9e363ffab25b57a56b318cc33baf6ff583af831ef5640def5dc06a62a4a7a3
ISICitedReferencesCount	237
ISICitedReferencesURI	http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000256694400011&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN	0895-7177
IngestDate	Mon Jul 21 09:17:05 EDT 2025 Sat Nov 29 06:30:23 EST 2025 Tue Nov 18 22:37:54 EST 2025 Fri Feb 23 02:25:04 EST 2024
IsDoiOpenAccess	true
IsOpenAccess	true
IsPeerReviewed	true
IsScholarly	true
Issue	3
Keywords	Delay differential equations Homotopy perturbation method Applications in mathematical biology and engineering Differential equation Numerical method Delay equation Perturbation method Numerical analysis Scientific computation Applied mathematics Homotopy Mathematical model Computer aided analysis
Language	English
License	http://www.elsevier.com/open-access/userlicense/1.0 https://www.elsevier.com/tdm/userlicense/1.0 https://www.elsevier.com/open-access/userlicense/1.0 CC BY 4.0
LinkModel	OpenURL
MergedId	FETCHMERGED-LOGICAL-c327t-75c9e363ffab25b57a56b318cc33baf6ff583af831ef5640def5dc06a62a4a7a3
OpenAccessLink	https://dx.doi.org/10.1016/j.mcm.2007.09.016
PageCount	13
ParticipantIDs	pascalfrancis_primary_20470560 crossref_citationtrail_10_1016_j_mcm_2007_09_016 crossref_primary_10_1016_j_mcm_2007_09_016 elsevier_sciencedirect_doi_10_1016_j_mcm_2007_09_016
PublicationCentury	2000
PublicationDate	2008-08-01
PublicationDateYYYYMMDD	2008-08-01
PublicationDate_xml	– month: 08 year: 2008 text: 2008-08-01 day: 01
PublicationDecade	2000
PublicationPlace	Oxford
PublicationPlace_xml	– name: Oxford
PublicationTitle	Mathematical and computer modelling
PublicationYear	2008
Publisher	Elsevier Ltd Elsevier Science
Publisher_xml	– name: Elsevier Ltd – name: Elsevier Science
References	He (b5) 2003; 135 Siddiqui, Zeb, Ghori, Benharbit (b17) 2008; 36 Cveticanin (b9) 2006; 30 He (b10) 2005; 26 M. Rafei, D.D. Ganji, H. Daniali, Solution of the epidemic model by homotopy perturbation method, Applied Mathematics and Computation (in press) Ganji, Sadighi (b11) 2007; 207 Shakeri, Dehghan (b21) 2007; 75 Dugard, Verriest (b2) 1997; vol. 228 Dehghan, Shakeri (b22) 2007; 75 Ganji, Rafei (b8) 2006; 356 A. Beléndez, T. Beléndez, A. Márquez, C. Neipp, Application of He’s homotopy perturbation method to conservative truly nonlinear oscillators, Chaos, Solitons and Fractals (in press) Dehghan, Shakeri (b24) 2008; 78 He (b3) 1999; 178 He (b4) 2000; 35 Ghasemi, Tavassoli Kajani, Babolian (b15) 2007; 188 Wang (b7) 2008; 35 Dehghan (b19) 2006; 71 A. Rajabi, Homotopy perturbation method for fin efficiency of convective straight fins with temperature-dependent thermal conductivity, Physics Letters A (in press) Chun (b18) 2007; 34 Kuang (b1) 1993 He (b6) 2006; 350 Dehghan (b20) 2006; 22 Chun, Ham (b13) 2006; 22 M. Dehghan, F. Shakeri, The use of He’s homotopy perturbation method for solving a partial differential equation arising in modeling of flow in porous media, Journal of Porous Media (2008) (in press) Cveticanin (10.1016/j.mcm.2007.09.016_b9) 2006; 30 Ghasemi (10.1016/j.mcm.2007.09.016_b15) 2007; 188 Siddiqui (10.1016/j.mcm.2007.09.016_b17) 2008; 36 Ganji (10.1016/j.mcm.2007.09.016_b11) 2007; 207 Dehghan (10.1016/j.mcm.2007.09.016_b22) 2007; 75 He (10.1016/j.mcm.2007.09.016_b6) 2006; 350 Dugard (10.1016/j.mcm.2007.09.016_b2) 1997; vol. 228 Kuang (10.1016/j.mcm.2007.09.016_b1) 1993 Ganji (10.1016/j.mcm.2007.09.016_b8) 2006; 356 Dehghan (10.1016/j.mcm.2007.09.016_b19) 2006; 71 He (10.1016/j.mcm.2007.09.016_b10) 2005; 26 Dehghan (10.1016/j.mcm.2007.09.016_b20) 2006; 22 He (10.1016/j.mcm.2007.09.016_b5) 2003; 135 Wang (10.1016/j.mcm.2007.09.016_b7) 2008; 35 10.1016/j.mcm.2007.09.016_b14 Chun (10.1016/j.mcm.2007.09.016_b18) 2007; 34 10.1016/j.mcm.2007.09.016_b16 Chun (10.1016/j.mcm.2007.09.016_b13) 2006; 22 Dehghan (10.1016/j.mcm.2007.09.016_b24) 2008; 78 He (10.1016/j.mcm.2007.09.016_b4) 2000; 35 Shakeri (10.1016/j.mcm.2007.09.016_b21) 2007; 75 He (10.1016/j.mcm.2007.09.016_b3) 1999; 178 10.1016/j.mcm.2007.09.016_b12 10.1016/j.mcm.2007.09.016_b23
References_xml	– volume: 22 start-page: 475 year: 2006 end-page: 487 ident: b13 article-title: Newton-like iteration methods for solving non-linear equations publication-title: Communications in Numerical Methods in Engineering – volume: 188 start-page: 450 year: 2007 end-page: 455 ident: b15 article-title: Numerical solutions of the nonlinear integro-differential equations: Wavelet-Galerkin method and homotopy perturbation method publication-title: Applied Mathematics and Computation – reference: M. Dehghan, F. Shakeri, The use of He’s homotopy perturbation method for solving a partial differential equation arising in modeling of flow in porous media, Journal of Porous Media (2008) (in press) – volume: 35 start-page: 843 year: 2008 end-page: 850 ident: b7 article-title: Homotopy perturbation method for fractional KdV–Burgers equation publication-title: Chaos, Solitons and Fractals – volume: 356 start-page: 131 year: 2006 end-page: 137 ident: b8 article-title: Solitary wave solutions for a generalized Hirota–Satsuma coupled KdV equation by homotopy perturbation method publication-title: Physics Letters A – reference: A. Beléndez, T. Beléndez, A. Márquez, C. Neipp, Application of He’s homotopy perturbation method to conservative truly nonlinear oscillators, Chaos, Solitons and Fractals (in press) – volume: 178 start-page: 257 year: 1999 end-page: 262 ident: b3 article-title: Homotopy perturbation technique publication-title: Computational Methods in Applied Mechanics and Engineering – volume: 35 start-page: 37 year: 2000 end-page: 43 ident: b4 article-title: A coupling method of a homotopy technique and a perturbation technique for non-linear problems publication-title: International Journal of Non-Linear Mechanics – volume: vol. 228 year: 1997 ident: b2 publication-title: Stability and Control of Time-delay Systems – volume: 36 start-page: 182 year: 2008 end-page: 192 ident: b17 article-title: Homotopy perturbation method for heat transfer flow of a third grade fluid between parallel plates publication-title: Chaos, Solitons and Fractals – volume: 30 start-page: 1221 year: 2006 end-page: 1230 ident: b9 article-title: Homotopy perturbation method for pure nonlinear differential equation publication-title: Chaos, Solitons and Fractals – reference: M. Rafei, D.D. Ganji, H. Daniali, Solution of the epidemic model by homotopy perturbation method, Applied Mathematics and Computation (in press) – volume: 207 start-page: 24 year: 2007 end-page: 34 ident: b11 article-title: Application of homotopy-perturbation and variational iteration methods to nonlinear heat transfer and porous media equations publication-title: Journal of Computational and Applied Mathematics – volume: 75 start-page: 551 year: 2007 end-page: 556 ident: b21 article-title: Inverse problem of diffusion equation by He’s homotopy perturbation method publication-title: Physica Scripta – volume: 75 start-page: 778 year: 2007 end-page: 787 ident: b22 article-title: Solution of a partial differential equation subject to temperature overspecification by He’s homotopy perturbation method publication-title: Physica Scripta – year: 1993 ident: b1 article-title: Delay Differential Equations with Applications in Population Dynamics – volume: 350 start-page: 87 year: 2006 end-page: 88 ident: b6 article-title: Homotopy perturbation method for solving boundary value problems publication-title: Physics Letters A – volume: 34 start-page: 1130 year: 2007 end-page: 1134 ident: b18 article-title: Integration using He’s homotopy perturbation method publication-title: Chaos, Solitons and Fractals – volume: 26 start-page: 695 year: 2005 end-page: 700 ident: b10 article-title: Application of homotopy perturbation method to nonlinear wave equations publication-title: Chaos, Solitons and Fractals – volume: 22 start-page: 220 year: 2006 end-page: 257 ident: b20 article-title: A computational study of the one-dimensional parabolic equation subject to nonclassical boundary specifications publication-title: Numerical Methods for Partial Differential Equations – reference: A. Rajabi, Homotopy perturbation method for fin efficiency of convective straight fins with temperature-dependent thermal conductivity, Physics Letters A (in press) – volume: 135 start-page: 73 year: 2003 end-page: 79 ident: b5 article-title: Homotopy perturbation method: A new nonlinear analytical technique publication-title: Applied Mathematics and Computation – volume: 71 start-page: 16 year: 2006 end-page: 30 ident: b19 article-title: Finite difference procedures for solving a problem arising in modeling and design of certain optoelectronic devices publication-title: Mathematics and Computers in Simulation – volume: 78 start-page: 361 year: 2008 end-page: 376 ident: b24 article-title: Solution of an integro-differential equation arising in oscillating magnetic fields using He’s homotopy perturbation method publication-title: Progress in Electromagnetics Research – volume: 207 start-page: 24 year: 2007 ident: 10.1016/j.mcm.2007.09.016_b11 article-title: Application of homotopy-perturbation and variational iteration methods to nonlinear heat transfer and porous media equations publication-title: Journal of Computational and Applied Mathematics doi: 10.1016/j.cam.2006.07.030 – volume: 356 start-page: 131 year: 2006 ident: 10.1016/j.mcm.2007.09.016_b8 article-title: Solitary wave solutions for a generalized Hirota–Satsuma coupled KdV equation by homotopy perturbation method publication-title: Physics Letters A doi: 10.1016/j.physleta.2006.03.039 – volume: 75 start-page: 778 year: 2007 ident: 10.1016/j.mcm.2007.09.016_b22 article-title: Solution of a partial differential equation subject to temperature overspecification by He’s homotopy perturbation method publication-title: Physica Scripta doi: 10.1088/0031-8949/75/6/007 – volume: 78 start-page: 361 year: 2008 ident: 10.1016/j.mcm.2007.09.016_b24 article-title: Solution of an integro-differential equation arising in oscillating magnetic fields using He’s homotopy perturbation method publication-title: Progress in Electromagnetics Research doi: 10.2528/PIER07090403 – volume: 34 start-page: 1130 year: 2007 ident: 10.1016/j.mcm.2007.09.016_b18 article-title: Integration using He’s homotopy perturbation method publication-title: Chaos, Solitons and Fractals doi: 10.1016/j.chaos.2006.04.019 – volume: 178 start-page: 257 year: 1999 ident: 10.1016/j.mcm.2007.09.016_b3 article-title: Homotopy perturbation technique publication-title: Computational Methods in Applied Mechanics and Engineering doi: 10.1016/S0045-7825(99)00018-3 – volume: 350 start-page: 87 year: 2006 ident: 10.1016/j.mcm.2007.09.016_b6 article-title: Homotopy perturbation method for solving boundary value problems publication-title: Physics Letters A doi: 10.1016/j.physleta.2005.10.005 – ident: 10.1016/j.mcm.2007.09.016_b14 doi: 10.1016/j.physleta.2006.11.062 – volume: 30 start-page: 1221 year: 2006 ident: 10.1016/j.mcm.2007.09.016_b9 article-title: Homotopy perturbation method for pure nonlinear differential equation publication-title: Chaos, Solitons and Fractals doi: 10.1016/j.chaos.2005.08.180 – volume: 188 start-page: 450 year: 2007 ident: 10.1016/j.mcm.2007.09.016_b15 article-title: Numerical solutions of the nonlinear integro-differential equations: Wavelet-Galerkin method and homotopy perturbation method publication-title: Applied Mathematics and Computation doi: 10.1016/j.amc.2006.10.001 – volume: 75 start-page: 551 year: 2007 ident: 10.1016/j.mcm.2007.09.016_b21 article-title: Inverse problem of diffusion equation by He’s homotopy perturbation method publication-title: Physica Scripta doi: 10.1088/0031-8949/75/4/031 – volume: 71 start-page: 16 year: 2006 ident: 10.1016/j.mcm.2007.09.016_b19 article-title: Finite difference procedures for solving a problem arising in modeling and design of certain optoelectronic devices publication-title: Mathematics and Computers in Simulation doi: 10.1016/j.matcom.2005.10.001 – ident: 10.1016/j.mcm.2007.09.016_b23 doi: 10.1615/JPorMedia.v11.i8.50 – volume: 22 start-page: 220 year: 2006 ident: 10.1016/j.mcm.2007.09.016_b20 article-title: A computational study of the one-dimensional parabolic equation subject to nonclassical boundary specifications publication-title: Numerical Methods for Partial Differential Equations doi: 10.1002/num.20071 – volume: 135 start-page: 73 year: 2003 ident: 10.1016/j.mcm.2007.09.016_b5 article-title: Homotopy perturbation method: A new nonlinear analytical technique publication-title: Applied Mathematics and Computation doi: 10.1016/S0096-3003(01)00312-5 – volume: 36 start-page: 182 year: 2008 ident: 10.1016/j.mcm.2007.09.016_b17 article-title: Homotopy perturbation method for heat transfer flow of a third grade fluid between parallel plates publication-title: Chaos, Solitons and Fractals doi: 10.1016/j.chaos.2006.06.037 – volume: vol. 228 year: 1997 ident: 10.1016/j.mcm.2007.09.016_b2 – volume: 26 start-page: 695 year: 2005 ident: 10.1016/j.mcm.2007.09.016_b10 article-title: Application of homotopy perturbation method to nonlinear wave equations publication-title: Chaos, Solitons and Fractals doi: 10.1016/j.chaos.2005.03.006 – volume: 22 start-page: 475 year: 2006 ident: 10.1016/j.mcm.2007.09.016_b13 article-title: Newton-like iteration methods for solving non-linear equations publication-title: Communications in Numerical Methods in Engineering doi: 10.1002/cnm.832 – volume: 35 start-page: 37 year: 2000 ident: 10.1016/j.mcm.2007.09.016_b4 article-title: A coupling method of a homotopy technique and a perturbation technique for non-linear problems publication-title: International Journal of Non-Linear Mechanics doi: 10.1016/S0020-7462(98)00085-7 – ident: 10.1016/j.mcm.2007.09.016_b16 doi: 10.1016/j.chaos.2006.09.070 – ident: 10.1016/j.mcm.2007.09.016_b12 doi: 10.1016/j.amc.2006.09.019 – year: 1993 ident: 10.1016/j.mcm.2007.09.016_b1 – volume: 35 start-page: 843 year: 2008 ident: 10.1016/j.mcm.2007.09.016_b7 article-title: Homotopy perturbation method for fractional KdV–Burgers equation publication-title: Chaos, Solitons and Fractals doi: 10.1016/j.chaos.2006.05.074
SSID	ssj0005908
Score	2.3713686
Snippet	Delay differential equations (denoted as DDE) have a wide range of application in science and engineering. They arise when the rate of change of a...
SourceID	pascalfrancis crossref elsevier
SourceType	Index Database Enrichment Source Publisher
StartPage	486
SubjectTerms	Applications in mathematical biology and engineering Delay differential equations Exact sciences and technology Homotopy perturbation method Mathematical analysis Mathematics Methods of scientific computing (including symbolic computation, algebraic computation) Numerical analysis Numerical analysis. Scientific computation Ordinary differential equations Sciences and techniques of general use
Title	Solution of delay differential equations via a homotopy perturbation method
URI	https://dx.doi.org/10.1016/j.mcm.2007.09.016
Volume	48
WOSCitedRecordID	wos000256694400011&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText	1
inHoldings	1
isFullTextHit
isPrint
journalDatabaseRights	– providerCode: PRVESC databaseName: Elsevier SD Freedom Collection Journals 2021 customDbUrl: eissn: 1872-9479 dateEnd: 20131231 omitProxy: false ssIdentifier: ssj0005908 issn: 0895-7177 databaseCode: AIEXJ dateStart: 19950101 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier
link	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV3Nb9MwFLdKxwGEEF8T42PygRMoUxrbsXOsoFAYmzgM1FvkOLa2qU3L2lXbf89z_NFswIADl7SxnKbK-_X559f33g-hV6rKcl6zOmG64gml2iRCkjSptNaCinog21qYb5_54aGYTIovvZ4JtTDrKW8acXFRLP6rqWEMjG1LZ__B3PFDYQDeg9HhCGaH418ZPgS6LA20LSAvowjKykbH9fdzn_22tvVYb45tOt58cWkbGMPyUzlAOGHpLnM9iP1dfXcB5fUgnJjONCyBNlozHu7D_rDlxUBlZzqGnN-Nxh_Gwzaz4EAf1ydXYg4iZrz5QFgohvH-p-uzCpbADpF3HSwVHSCFoh7nL2nog-3OnCD1T17dBRhO92Zq5ptOFnvp4BcdtK-tbDHfMEspB6aX3kJbGWeF6KOt4cfR5NMmGahotQvj1w__f7eZgNdu-zsGc28hl2AC4wRROizl6AG677cXeOhg8RD1dPMI3e00nYSzjSWXj9F-gAueG9zCBXfhgiNcMMAFSxzggrtwwQ4uT9DX96Ojt-PEC2wkimR8lXCmCk1yYoysMlYxLllegZNXipBKmtwYJog0ggy0YTlNa3ipVZrLPJNUckm2Ub-ZN_opwnUha9ibSkLMgFqZs0qRgYTZhmggPHQHpeGhlcp3n7ciKNMypBmelvCcrSoqL9OihJEd9DpesnCtV26aTIMlSs8dHScsAUQ3XbZ7xWrxRgExz_404Tm6s_mFvED91dm5foluq_XqZHm263H2A69TmrI
linkProvider	Elsevier
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=Solution+of+delay+differential+equations+via+a+homotopy+perturbation+method&rft.jtitle=Mathematical+and+computer+modelling&rft.au=SHAKERI%2C+Fatemeh&rft.au=DEHGHAN%2C+Mehdi&rft.date=2008-08-01&rft.pub=Elsevier+Science&rft.issn=0895-7177&rft.volume=48&rft.issue=3-4&rft.spage=486&rft.epage=498&rft_id=info:doi/10.1016%2Fj.mcm.2007.09.016&rft.externalDBID=n%2Fa&rft.externalDocID=20470560
thumbnail_l	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0895-7177&client=summon
thumbnail_m	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0895-7177&client=summon
thumbnail_s	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0895-7177&client=summon