Efficient spectral-Petrov-Galerkin methods for third- and fifth-order differential equations using general parameters generalized Jacobi polynomials
Two new families of general parameters generalized Jacobi polynomials are introduced. Some efficient and accurate algorithms based on these families are developed and implemented for solving third- and fifth-order differential equations in one variable subject to homogeneous and nonhomogeneous bound...
Saved in:
| Published in | Quaestiones mathematicae Vol. 36; no. 1; pp. 15 - 38 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Grahamstown
Taylor & Francis Group
01.03.2013
Taylor & Francis Ltd |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1607-3606 1727-933X |
| DOI | 10.2989/16073606.2013.779945 |
Cover
| Abstract | Two new families of general parameters generalized Jacobi polynomials are introduced. Some efficient and accurate algorithms based on these families are developed and implemented for solving third- and fifth-order differential equations in one variable subject to homogeneous and nonhomogeneous boundary conditions using a dual Petrov-Galerkin method. The use of general parameters generalized Jacobi polynomials leads to simplified analysis, more precise error estimates and well conditioned algorithms. The method leads to linear systems with specially structured matrices that can be efficiently inverted. Numerical results indicating the high accuracy and effectiveness of the proposed algorithms are presented. |
|---|---|
| AbstractList | Two new families of general parameters generalized Jacobi polynomials are introduced. Some efficient and accurate algorithms based on these families are developed and implemented for solving third- and fifth-order differential equations in one variable subject to homogeneous and nonhomogeneous boundary conditions using a dual Petrov-Galerkin method. The use of general parameters generalized Jacobi polynomials leads to simplified analysis, more precise error estimates and well conditioned algorithms. The method leads to linear systems with specially structured matrices that can be efficiently inverted. Numerical results indicating the high accuracy and effectiveness of the proposed algorithms are presented. [PUBLICATION ABSTRACT] Two new families of general parameters generalized Jacobi polynomials are introduced. Some efficient and accurate algorithms based on these families are developed and implemented for solving third- and fifth-order differential equations in one variable subject to homogeneous and nonhomogeneous boundary conditions using a dual Petrov-Galerkin method. The use of general parameters generalized Jacobi polynomials leads to simplified analysis, more precise error estimates and well conditioned algorithms. The method leads to linear systems with specially structured matrices that can be efficiently inverted. Numerical results indicating the high accuracy and effectiveness of the proposed algorithms are presented. |
| Author | Abd-Elhameed, W.M. Doha, E.H. Youssri, Y.H. |
| Author_xml | – sequence: 1 givenname: W.M. surname: Abd-Elhameed fullname: Abd-Elhameed, W.M. email: walee_9@yahoo.com organization: Department of Mathematics, Faculty of Science , Cairo University – sequence: 2 givenname: E.H. surname: Doha fullname: Doha, E.H. organization: Department of Mathematics, Faculty of Science , Cairo University – sequence: 3 givenname: Y.H. surname: Youssri fullname: Youssri, Y.H. organization: Department of Mathematics, Faculty of Science , Cairo University |
| BookMark | eNqFkc1u1DAURi1UJNrCG7CwxIZNpv5J4pgNQlVpQZVgARI7y0muOy6JnV47RcNz8MB4GLrpAlbXss53ZN_vhByFGICQl5xthO70GW-Zki1rN4JxuVFK67p5Qo65EqrSUn47KueCVHvmGTlJ6ZYx2TCuj8mvC-f84CFkmhYYMtqp-gwZ4311aSfA7z7QGfI2jom6iDRvPY4VtWGkzru8rSKOgHT0zgEWi7cThbvVZh9Domvy4YbeQIDipYtFW1yA6eHK_4SRfrRD7D1d4rQLcS6C9Jw8dWXAi7_zlHx9f_Hl_Kq6_nT54fzddTXItsuV7uvWdlxapVre950VTfmhFg0IyQSrxahZLx0fRMec5RJ4p2ruGqUb0ErV8pS8PngXjHcrpGxmnwaYJhsgrsnwVvG6FXWnCvrqEXobVwzldYZLIbuG63ovfHOgBowpITgz-PxnF2WxfjKcmX1h5qEwsy_MHAor4fpReEE_W9z9L_b2EPOhFDTbHxGn0WS7myI6tGHwych_Gn4D2VqwRQ |
| CitedBy_id | crossref_primary_10_1007_s00009_017_0973_z crossref_primary_10_1155_2014_309264 crossref_primary_10_1016_j_jare_2014_03_003 crossref_primary_10_1140_epjp_i2016_16012_0 crossref_primary_10_1007_s11071_017_3519_9 crossref_primary_10_1007_s40819_019_0729_5 crossref_primary_10_1080_00207160_2017_1410544 crossref_primary_10_1155_2013_542839 crossref_primary_10_1142_S0219876218501189 crossref_primary_10_1155_2015_672703 crossref_primary_10_1016_j_joems_2016_07_001 crossref_primary_10_3103_S1068362314060065 crossref_primary_10_1007_s40840_017_0491_y crossref_primary_10_15388_NA_2019_3_2 crossref_primary_10_1155_2013_715756 crossref_primary_10_3390_e18100345 crossref_primary_10_1080_10652469_2015_1029924 crossref_primary_10_1155_2014_456501 crossref_primary_10_1007_s10092_016_0176_1 crossref_primary_10_1016_j_joems_2014_04_008 crossref_primary_10_1007_s13324_017_0183_7 crossref_primary_10_1142_S0219876217500839 crossref_primary_10_1115_1_4046879 crossref_primary_10_1002_num_22074 crossref_primary_10_3934_math_2022789 crossref_primary_10_1002_mma_3277 crossref_primary_10_1007_s40819_017_0388_3 crossref_primary_10_1016_S0252_9602_15_60004_2 crossref_primary_10_1155_2014_626275 crossref_primary_10_1186_s13662_019_2402_z crossref_primary_10_1186_s13662_017_1336_6 crossref_primary_10_1002_num_22756 crossref_primary_10_32513_tbilisi_1529460019 crossref_primary_10_1007_s11139_014_9668_2 crossref_primary_10_1155_2014_636191 crossref_primary_10_1007_s40096_015_0155_8 crossref_primary_10_1007_s40819_021_01115_1 crossref_primary_10_1007_s40314_018_0633_3 crossref_primary_10_1007_s40819_016_0157_8 crossref_primary_10_1016_j_joems_2015_05_002 crossref_primary_10_1186_s13661_015_0364_y crossref_primary_10_3390_fractalfract7020133 crossref_primary_10_1140_epjp_i2015_15052_2 |
| Cites_doi | 10.1007/978-94-009-3715-4 10.1088/0305-4470/35/15/308 10.1007/s11075-006-9034-6 10.1137/S0036142900378327 10.1017/CBO9781107325937 10.1017/S1446181100003540 10.1088/0305-4470/37/3/010 10.1007/978-3-642-84108-8 10.1137/S1064827500378933 10.1137/S0036142999361505 10.1016/j.matcom.2009.03.011 10.1016/j.apnum.2007.07.001 10.1007/978-3-540-46783-0 10.1137/0729094 10.1006/jcph.1993.1065 10.1016/j.apm.2008.05.005 10.1007/s10915-005-9055-7 |
| ContentType | Journal Article |
| Copyright | Copyright NISC Pty Ltd 2013 Copyright NISC Pty Ltd |
| Copyright_xml | – notice: Copyright NISC Pty Ltd 2013 – notice: Copyright NISC Pty Ltd |
| DBID | AAYXX CITATION 7SC 7TB 8FD FR3 JQ2 KR7 L7M L~C L~D |
| DOI | 10.2989/16073606.2013.779945 |
| DatabaseName | CrossRef Computer and Information Systems Abstracts Mechanical & Transportation Engineering Abstracts Technology Research Database Engineering Research Database ProQuest Computer Science Collection Civil Engineering Abstracts Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional |
| DatabaseTitle | CrossRef Civil Engineering Abstracts Technology Research Database Computer and Information Systems Abstracts – Academic Mechanical & Transportation Engineering Abstracts ProQuest Computer Science Collection Computer and Information Systems Abstracts Engineering Research Database Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Professional |
| DatabaseTitleList | Civil Engineering Abstracts |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics |
| EISSN | 1727-933X |
| EndPage | 38 |
| ExternalDocumentID | 2936611531 10_2989_16073606_2013_779945 779945 |
| Genre | Feature |
| GroupedDBID | .7F .QJ 0BK 0R~ 123 29P 30N 4.4 4JU AAENE AAGDL AAHIA AAJMT AALDU AAMIU AAPUL AAQRR ABCCY ABFIM ABHAV ABJNI ABLIJ ABPAQ ABPEM ABTAI ABXUL ABXYU ACGFS ACIWK ACTIO ADCVX ADGTB AEISY AENEX AEOZL AEPSL AEYOC AFRVT AGDLA AGMYJ AHDZW AIJEM AIYEW AKBVH AKOOK ALMA_UNASSIGNED_HOLDINGS ALQZU AMVHM ANHLU AQRUH AQTUD AVBZW AWYRJ BLEHA CCCUG CE4 CS3 DGEBU DKSSO DU5 EBS EJD E~A E~B GTTXZ H13 HZ~ H~P IPNFZ J.P KWQ KYCEM M4Z NA5 NY~ O9- P2P RIG RNANH ROSJB RTWRZ S-T SNACF TASJS TBQAZ TDBHL TEJ TFL TFT TFW TTHFI TUROJ UT5 UU3 ZGOLN ~S~ 07G AAIKQ AAKBW AAYXX ACAGQ ACGEE ACTCW AEUMN AGCQS AGLEN AGROQ AHMOU ALCKM AMEWO AMXXU BCCOT BPLKW C06 CITATION CRFIH DMQIW DWIFK IVXBP LJTGL NUSFT QCRFL TAQ TFMCV TOXWX UB9 V3K 7SC 7TB 8FD FR3 JQ2 KR7 L7M L~C L~D |
| ID | FETCH-LOGICAL-c368t-9b46a813a7761bb8a25360925e2302042d90b3f1c280fa13e18741f5795e97743 |
| ISSN | 1607-3606 |
| IngestDate | Thu Oct 02 10:31:06 EDT 2025 Wed Aug 13 08:14:58 EDT 2025 Wed Oct 01 02:23:44 EDT 2025 Thu Apr 24 23:01:28 EDT 2025 Mon Oct 20 23:39:20 EDT 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 1 |
| Language | English |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c368t-9b46a813a7761bb8a25360925e2302042d90b3f1c280fa13e18741f5795e97743 |
| Notes | SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 ObjectType-Article-1 ObjectType-Feature-2 content type line 23 |
| PQID | 1323851944 |
| PQPubID | 436421 |
| PageCount | 24 |
| ParticipantIDs | proquest_journals_1323851944 crossref_primary_10_2989_16073606_2013_779945 informaworld_taylorfrancis_310_2989_16073606_2013_779945 crossref_citationtrail_10_2989_16073606_2013_779945 proquest_miscellaneous_1671462487 |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | 2013-03-00 |
| PublicationDateYYYYMMDD | 2013-03-01 |
| PublicationDate_xml | – month: 03 year: 2013 text: 2013-03-00 |
| PublicationDecade | 2010 |
| PublicationPlace | Grahamstown |
| PublicationPlace_xml | – name: Grahamstown |
| PublicationTitle | Quaestiones mathematicae |
| PublicationYear | 2013 |
| Publisher | Taylor & Francis Group Taylor & Francis Ltd |
| Publisher_xml | – name: Taylor & Francis Group – name: Taylor & Francis Ltd |
| References | Doha E.H. (CIT0011) 2006; 42 Huang W.Z. (CIT0017) 1992; 29 Swanson C.A. (CIT0022) 1968 Andrews G.E. (CIT0002) 1999 Gregus M. (CIT0015) 1987 Merryfield W.J. (CIT0021) 1993; 105 Doha E.H. (CIT0012) 2007; 48 Doha E.H. (CIT0010) Szegö G. (CIT0023) 1985; 23 Funaro D. (CIT0014) 1992 Boyd J.P. (CIT0003) 2001 CIT0005 CIT0016 CIT0004 Doha E.H. (CIT0008) 2009; 79 CIT0007 Abramowitz M. (CIT0001) 1970; 55 CIT0006 Doha E.H. (CIT0013) 2008; 58 Doha E.H. (CIT0009) 2009; 33 Ma H. (CIT0018) 2000; 38 CIT0019 Mckelvey Ed (CIT0020) 1970 |
| References_xml | – volume-title: Lectures on Ordinary Differential Equation year: 1970 ident: CIT0020 – volume-title: Third Order Linear Differential Equations year: 1987 ident: CIT0015 doi: 10.1007/978-94-009-3715-4 – ident: CIT0005 doi: 10.1088/0305-4470/35/15/308 – volume: 42 start-page: 137 year: 2006 ident: CIT0011 publication-title: Numer. Algor. doi: 10.1007/s11075-006-9034-6 – ident: CIT0019 doi: 10.1137/S0036142900378327 – volume-title: Special Functions year: 1999 ident: CIT0002 doi: 10.1017/CBO9781107325937 – volume: 48 start-page: 361 year: 2007 ident: CIT0012 publication-title: ANZIAM J. doi: 10.1017/S1446181100003540 – ident: CIT0006 doi: 10.1088/0305-4470/37/3/010 – ident: CIT0004 doi: 10.1007/978-3-642-84108-8 – ident: CIT0007 doi: 10.1137/S1064827500378933 – volume: 38 start-page: 1425 year: 2000 ident: CIT0018 publication-title: SIAM J. Numer. Anal. doi: 10.1137/S0036142999361505 – volume: 79 start-page: 3221 year: 2009 ident: CIT0008 publication-title: Math. Comput. Simulat. doi: 10.1016/j.matcom.2009.03.011 – ident: CIT0010 publication-title: Collect. Math – volume: 55 volume-title: Handbook of Mrathematical Functions year: 1970 ident: CIT0001 – volume-title: Chebyshev and Fourier Spectral Methods year: 2001 ident: CIT0003 – volume: 58 start-page: 1224 year: 2008 ident: CIT0013 publication-title: Appl. Numer. Math. doi: 10.1016/j.apnum.2007.07.001 – volume-title: Polynomial Approximation of Differential Equations year: 1992 ident: CIT0014 doi: 10.1007/978-3-540-46783-0 – volume: 29 start-page: 1626 year: 1992 ident: CIT0017 publication-title: SIAM J. Numer. Anal. doi: 10.1137/0729094 – volume: 105 start-page: 182 year: 1993 ident: CIT0021 publication-title: J. Comput. Phys. doi: 10.1006/jcph.1993.1065 – volume: 33 start-page: 1982 year: 2009 ident: CIT0009 publication-title: Appl. Math. Model. doi: 10.1016/j.apm.2008.05.005 – volume: 23 volume-title: Orthogonal Polynomials year: 1985 ident: CIT0023 – ident: CIT0016 doi: 10.1007/s10915-005-9055-7 – volume-title: Comparison and Oscillation Theory of Linear Differential Equations year: 1968 ident: CIT0022 |
| SSID | ssj0035019 |
| Score | 2.106918 |
| Snippet | Two new families of general parameters generalized Jacobi polynomials are introduced. Some efficient and accurate algorithms based on these families are... |
| SourceID | proquest crossref informaworld |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 15 |
| SubjectTerms | Algorithms Differential equations Dual-Petrov-Galerkin method Error analysis general parameters generalized Jacobi polynomials Linear systems Mathematical models Methods nonhomogeneous Dirichlet conditions Polynomials Spectra Structured matrices Studies |
| Title | Efficient spectral-Petrov-Galerkin methods for third- and fifth-order differential equations using general parameters generalized Jacobi polynomials |
| URI | https://www.tandfonline.com/doi/abs/10.2989/16073606.2013.779945 https://www.proquest.com/docview/1323851944 https://www.proquest.com/docview/1671462487 |
| Volume | 36 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVEBS databaseName: EBSCOhost Mathematics Source - trial do 30.11.2025 customDbUrl: eissn: 1727-933X dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0035019 issn: 1607-3606 databaseCode: AMVHM dateStart: 19760101 isFulltext: true titleUrlDefault: https://www.ebsco.com/products/research-databases/mathematics-source providerName: EBSCOhost – providerCode: PRVLSH databaseName: aylor and Francis Online customDbUrl: mediaType: online eissn: 1727-933X dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0035019 issn: 1607-3606 databaseCode: AHDZW dateStart: 19970101 isFulltext: true providerName: Library Specific Holdings – providerCode: PRVAWR databaseName: Taylor & Francis Science and Technology Library-DRAA customDbUrl: eissn: 1727-933X dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0035019 issn: 1607-3606 databaseCode: 30N dateStart: 19970101 isFulltext: true titleUrlDefault: http://www.tandfonline.com/page/title-lists providerName: Taylor & Francis |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1LbxMxELZCeoED4ikCBRmJniqH7HpfPlY0IaraIqREDVws78M0Upq22Q0S_R38Lf4TM7az2dBSHpdV5M06m51vZ8bjmW8IeaMTHfI0C5kvdMgCMKksEZqzDFmxvZTruIeFwkfH0XAcHEzCSav1o5G1tKzSbnZ1Y13J_0gVxkCuWCX7D5KtJ4UB-AzyhSNIGI5_JeO-4X_A3XxTMLlQM4Ydss6_sveg9zEK7jpEly6bcLrImdku0FNdnTLDu1n3SKkweF5cLl1y3NJEEb5YWupdpAg_w9SZcjU0vQJf9QAUajrFVg_fsL5Zzcqmt_sRd5QMF1K5e1bzw6o1ytKc9WenMLENuZ5015Hzc7sT1e8OG4oJDLrJPvjkRl24AltH8Ga4YnStc0gjfQkVcIRx06jn6LHtGPhYTHDTN7jW2pY2ZQOdVgXb6tBfLQMSzWOQAqbH2TGnj3fjWAhLZrlJxH38QQ7Gh4dy1J-MNs8aww8eEng1YCq8HT64uGTYwgy3-nf4vsXYHbLlg5HptcnW3nD_88nKNcBNXFyP1X_S1nLivb296c42fKUNJt1rnoNxh0YPyH23jqF7FpQPSauYPyL3jmohl4_J9xqe9HfwpA6eFH6TWnhSgCdtwJM24UlreFIDT-qwSNfwpA14UgtP2oDnEzIe9Efvhsw1AWEZj5KKiTSIVOJxFceRl6aJ8kN4TMIPC1g8-2ByctEDleJlftLTyuMFNpn0dBiLsMC1DX9K2nPA-TNChQ7yUCsQQyaCnAdKZbmIFdeZ56uYpx3CV49bZo4hHxu1zCSslFFIciUkiUKSVkgdwuqrLixDzB--nzQlKSvzRmj7Mkh--6XbK6lLp4ZK6XHwumEdFgQd8ro-DUYCd_7UvIB3EyaLwSPygyR-fvsUL8jd9Uu7TdrVYlm8BK-7Sl85LP8E5vHZBQ |
| linkProvider | Library Specific Holdings |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1Lb9QwELagHKCH8la3FDASVy-b2I7jI0ItS-nuqZW4WXZityu2u-0mi0R_Bz-YGTtZURAgwTWxEz_GM2N75vsIeR3KILmrJMt1kEyASWWlDpxViIqdOR7UCBOFJ9NifCqOPsk-mrDpwipxDx0SUETU1bi48TA6xi3rUr9BUDQOnjdGZvGhUloLeZvckeDrI4kBH017ZYzXZugBYw2GVVL23G-_csM63cAu_UVXRwN0eJ-4vukp7uTzcN26YXX9E6rjf_XtAdnp3FP6NsnTQ3LLLx6R7ckG27V5TL4dRNQJMFY0pmmu7JwhL9fyC3sP1gbP3mnipW4odIy257NVzSi0iIZZaM9ZRPukPTMLaJg59VcJcbyhGId_Rs8SGDZFYPILDNhp-keza1_TI1DjbkYvl_OvmFUNK-gJOT08OHk3Zh23A6t4UbZMO1HYMuNWqSJzrrS5hF7rXHrYE-WgSWo9AknJqrwcBZtxj9yBWZBKS48uK39KthbLhd8lVAdRy2Bhristai6srWqtLA9VllvF3YDwfk5N1QGfI__G3MAGCMfc9GNucMxNGvMBYZtalwn44y_lyx_FxbTxwCUkdhTD_1x1vxct02mQxmQcnClwr4UYkFeb17D28ULHLvxyDWUKBYYuhz3n3r___SW5Oz6ZHJvjD9OPz8i9PNJ9YIzdPtlqV2v_HJyu1r2Iy-o7wxUgeQ |
| linkToPdf | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LbxMxELagSAgOvBGBAkbi6pBd2-v1EUFDKTTiQKXeLNtrtxEhCdkNEv0d_GBm7GzUggAJrrueXb_mZc98Q8jzWEfJnZes1FEyASqV1Tpy5hEVu3A8qhEmCh9Oqv0jcXAsj89l8WNYJfrQMQNFJFmNzL1sYgpb1rV-gZhoHAxvDMziQ6W0FvIyuVLhpRgmcYwmvSzGWzM0gJGCIUlOnvvtVy4opwvQpb-I6qR_xjeJ7Xuew04-DdedG_qzn0Ad_2dot8iNjXFKX-bddJtcCvM75PrhFtm1vUu-7yXMCVBVNCVpruyMYVWuxVf2BnQNnrzTXJW6pTAu2p1OVw2j0CEap7E7ZQnrk_Z1WUC-zGj4kvHGW4pR-Cf0JENhU4Ql_4zhOm3_aHoWGnoAQtxN6XIx-4Y51cA_98jReO_jq322qezAPK_qjmknKlsX3CpVFc7VtpQwal3KAB5RCXKk0SPYJ4Uv61G0BQ9YObCIUmkZ0GDl98nOfDEPDwjVUTQyWlhqr0XDhbW-0cry6IvSKu4GhPdLavwG9hyrb8wMuD8456afc4NzbvKcDwjbUi0z7Mdf2tfnd4vp0nFLzLVRDP8z6W6_s8xGfrSm4GBKgXEtxIA8274GzsfrHDsPizW0qRSouRI8zof__ven5OqH12Pz_u3k3SNyrUy1PjDAbpfsdKt1eAwWV-eeJKb6ARi_Hx0 |
| 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=Efficient+spectral-Petrov-Galerkin+methods+for+third-+and+fifth-order+differential+equations+using+general+parameters+generalized+Jacobi+polynomials&rft.jtitle=Quaestiones+mathematicae&rft.au=Abd-Elhameed%2C+W.M&rft.au=Doha%2C+E.H&rft.au=Youssri%2C+Y.H&rft.date=2013-03-01&rft.pub=Taylor+%26+Francis+Ltd&rft.issn=1607-3606&rft.eissn=1727-933X&rft.volume=36&rft.issue=1&rft.spage=15&rft_id=info:doi/10.2989%2F16073606.2013.779945&rft.externalDBID=NO_FULL_TEXT&rft.externalDocID=2936611531 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1607-3606&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1607-3606&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1607-3606&client=summon |