Numerical solution of singular regular boundary value problems by pole detection with qd-algorithm
In this paper, we present a method using qd-algorithm combined with finite difference method for numerically solving singular boundary value problems for certain ordinary differential equation having singular coefficients. (We can also use qd-algorithm combined with other numerical methods.) These p...
Saved in:
| Published in: | Journal of computational and applied mathematics Vol. 233; no. 2; pp. 420 - 436 |
|---|---|
| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Kidlington
Elsevier B.V
15.11.2009
Elsevier |
| Subjects: | |
| ISSN: | 0377-0427, 1879-1778 |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Abstract | In this paper, we present a method using qd-algorithm combined with finite difference method for numerically solving singular boundary value problems for certain ordinary differential equation having singular coefficients. (We can also use qd-algorithm combined with other numerical methods.)
These problems arise when reducing partial differential equation to ordinary differential equation by physical symmetry. Some illustrative examples are given to demonstrate the efficiency and high accuracy of the proposed method and compare it to the numerical results made with other methods. |
|---|---|
| AbstractList | In this paper, we present a method using qd-algorithm combined with finite difference method for numerically solving singular boundary value problems for certain ordinary differential equation having singular coefficients. (We can also use qd-algorithm combined with other numerical methods.)
These problems arise when reducing partial differential equation to ordinary differential equation by physical symmetry. Some illustrative examples are given to demonstrate the efficiency and high accuracy of the proposed method and compare it to the numerical results made with other methods. In this paper, we present a method using qd-algorithm combined with finite difference method for numerically solving singular boundary value problems for certain ordinary differential equation having singular coefficients. (We can also use qd-algorithm combined with other numerical methods.) These problems arise when reducing partial differential equation to ordinary differential equation by physical symmetry. Some illustrative examples are given to demonstrate the efficiency and high accuracy of the proposed method and compare it to the numerical results made with other methods. |
| Author | Marhraoui, N. Allouche, H. |
| Author_xml | – sequence: 1 givenname: H. surname: Allouche fullname: Allouche, H. email: allouche_hassane@yahoo.fr – sequence: 2 givenname: N. surname: Marhraoui fullname: Marhraoui, N. email: nmarhraoui@yahoo.fr |
| BackLink | http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=21980481$$DView record in Pascal Francis |
| BookMark | eNp9kD1v2zAQQIkiAeo4-QHduKSbVJISP4RMhdE2BYJmSWaCoo4pDUq0SSlF_n3oOMjQwdNxeO_AexfobIoTIPSFkpoSKr5ta2vGmhHS1UTWpBGf0Ioq2VVUSnWGVqSRsiItk5_RRc5bQojoaLtC_Z9lhOStCTjHsMw-Tjg6nP30tASTcILj7OMyDSa94GcTFsC7FPsAY8b9C97FAHiAGeyb_c_Pf_F-qEx4iqm8x0t07kzIcPU-1-jx54-HzW11d__r9-b7XWUbruZKStEJN_CWK6aAiQEcZ67horcGBtMxQVXfcgDOeC-tayVhtnO8EwUnRjZr9PW4t3xuv0Ce9eizhRDMBHHJumml4oryAl6_gyaXw10yk_VZ75Ify4Wa0U6RVtHC0SNnU8w5gftAKNGH6nqrS3V9qK6J1KV6ceR_jvWzOYSZk_HhpHlzNKE0evaQdLYeJguDTyWtHqI_Yb8CXWuf8w |
| CODEN | JCAMDI |
| CitedBy_id | crossref_primary_10_1016_j_cam_2013_07_050 crossref_primary_10_1007_s00009_019_1342_x crossref_primary_10_1016_j_apnum_2021_03_010 crossref_primary_10_1016_j_cam_2016_08_003 |
| Cites_doi | 10.1016/j.amc.2003.07.020 10.1093/imamat/13.3.379 10.1007/BF02165591 10.1016/j.advengsoft.2008.04.010 10.1016/j.matcom.2006.09.006 10.1007/BF01436387 10.1007/BF01396339 10.1002/sapm1959381209 10.1088/0305-4470/18/12/011 10.1016/j.amc.2003.12.004 10.1016/S0096-3003(02)00613-6 10.1016/0017-9310(79)90202-3 10.1088/0305-4470/20/6/024 |
| ContentType | Journal Article |
| Copyright | 2009 Elsevier B.V. 2009 INIST-CNRS |
| Copyright_xml | – notice: 2009 Elsevier B.V. – notice: 2009 INIST-CNRS |
| DBID | 6I. AAFTH AAYXX CITATION IQODW 7SC 7TB 8FD FR3 JQ2 KR7 L7M L~C L~D |
| DOI | 10.1016/j.cam.2009.07.036 |
| DatabaseName | ScienceDirect Open Access Titles Elsevier:ScienceDirect:Open Access CrossRef Pascal-Francis 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 | 1879-1778 |
| EndPage | 436 |
| ExternalDocumentID | 21980481 10_1016_j_cam_2009_07_036 S0377042709004403 |
| GroupedDBID | --K --M -~X .~1 0R~ 1B1 1RT 1~. 1~5 29K 4.4 457 4G. 5GY 5VS 6I. 7-5 71M 8P~ 9JN AABNK AACTN AAEDT AAEDW AAFTH AAFWJ AAIAV AAIKJ AAKOC AALRI AAOAW AAQFI AAQXK AAXUO ABAOU ABEFU ABFNM ABJNI ABMAC ABTAH ABVKL ABXDB ABYKQ ACAZW ACDAQ ACGFS ACRLP ADBBV ADEZE ADMUD AEBSH AEKER AENEX AEXQZ AFKWA AFTJW AGHFR AGUBO AGYEJ AHHHB AIEXJ AIGVJ AIKHN AITUG AJBFU AJOXV ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ ARUGR ASPBG AVWKF AXJTR AZFZN BKOJK BLXMC CS3 D-I DU5 EBS EFJIC EFLBG EJD EO8 EO9 EP2 EP3 F5P FDB FEDTE FGOYB FIRID FNPLU FYGXN G-2 G-Q G8K GBLVA HVGLF HZ~ IHE IXB J1W KOM LG9 M26 M41 MHUIS MO0 N9A NCXOZ NHB O-L O9- OAUVE OK1 OZT P-8 P-9 P2P PC. Q38 R2- RIG RNS ROL RPZ SDF SDG SDP SES SEW SPC SPCBC SSW SSZ T5K TN5 UPT WUQ XPP YQT ZMT ZY4 ~02 ~G- 9DU AATTM AAXKI AAYWO AAYXX ABDPE ABWVN ACLOT ACRPL ACVFH ADCNI ADNMO ADVLN AEIPS AEUPX AFJKZ AFPUW AGQPQ AIGII AIIUN AKBMS AKRWK AKYEP ANKPU APXCP CITATION EFKBS ~HD AFXIZ AGCQF AGRNS BNPGV IQODW SSH 7SC 7TB 8FD FR3 JQ2 KR7 L7M L~C L~D |
| ID | FETCH-LOGICAL-c358t-77696fd545828e26def52f356bcaeda92618b45ee525b7cf4702c9f59628e0a73 |
| ISICitedReferencesCount | 4 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000270619900031&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0377-0427 |
| IngestDate | Wed Oct 01 12:34:04 EDT 2025 Mon Jul 21 09:16:58 EDT 2025 Sat Nov 29 06:07:30 EST 2025 Tue Nov 18 22:24:54 EST 2025 Fri Feb 23 02:27:52 EST 2024 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 2 |
| Keywords | 65L06 Singularity Boundary value problems 65L07 Degenerate problems Fröbenius method Finite difference scheme Formally orthogonal Hadamard polynomials 65L Except 65L05 65L70 65L80 65L20 65L12 Pole detection qd-Algorithm Difference scheme Differential equation Singular equation Singular value Numerical method Partial differential equation Numerical solution Initial value problem Regular solution Algorithm Orthogonal polynomial Degenerate equation Numerical analysis Boundary value problem Applied mathematics Problem solving Finite difference method |
| 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-c358t-77696fd545828e26def52f356bcaeda92618b45ee525b7cf4702c9f59628e0a73 |
| Notes | ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23 |
| OpenAccessLink | https://dx.doi.org/10.1016/j.cam.2009.07.036 |
| PQID | 34785815 |
| PQPubID | 23500 |
| PageCount | 17 |
| ParticipantIDs | proquest_miscellaneous_34785815 pascalfrancis_primary_21980481 crossref_primary_10_1016_j_cam_2009_07_036 crossref_citationtrail_10_1016_j_cam_2009_07_036 elsevier_sciencedirect_doi_10_1016_j_cam_2009_07_036 |
| PublicationCentury | 2000 |
| PublicationDate | 2009-11-15 |
| PublicationDateYYYYMMDD | 2009-11-15 |
| PublicationDate_xml | – month: 11 year: 2009 text: 2009-11-15 day: 15 |
| PublicationDecade | 2000 |
| PublicationPlace | Kidlington |
| PublicationPlace_xml | – name: Kidlington |
| PublicationTitle | Journal of computational and applied mathematics |
| PublicationYear | 2009 |
| Publisher | Elsevier B.V Elsevier |
| Publisher_xml | – name: Elsevier B.V – name: Elsevier |
| References | Kadalbajoo, Aggarwal (b19) 2004; 156 Jamet (b5) 1970; 14 Cohen, Jones (b8) 1974; 13 Kadalbajoo, Aggarwal (b10) 2005; 160 Weinitschke (b2) 1958; 38 Schneider (b1) 1979; 23 Coddington, Levinson (b14) 1955 Fuchs (b13) 1905; 141 Killingbeck (b4) 1987; 20 Rutishauser (b15) 1957 Reddien (b9) 1975; 25 Holubec, Stauffer (b3) 1985; 18 Xian-Fan (b7) 2007; 75 H. Allouche, A. Cuyt, Reliable pole detection using a deflated qd-algorithm: When Bernoulli, Hadamard and Rutishauser cooperate, Numer. Math. (in press) Baker, Graves-Morris (b17) 1981 Kumar, Singh (b11) 2009; 40 Gustafsson (b6) 1973; 21 Ravi Kanth, Reddy (b18) 2003; 146 Henrici (b12) 1974; vol. I Xian-Fan (10.1016/j.cam.2009.07.036_b7) 2007; 75 Henrici (10.1016/j.cam.2009.07.036_b12) 1974; vol. I Cohen (10.1016/j.cam.2009.07.036_b8) 1974; 13 Reddien (10.1016/j.cam.2009.07.036_b9) 1975; 25 Kadalbajoo (10.1016/j.cam.2009.07.036_b19) 2004; 156 Kadalbajoo (10.1016/j.cam.2009.07.036_b10) 2005; 160 10.1016/j.cam.2009.07.036_b16 Holubec (10.1016/j.cam.2009.07.036_b3) 1985; 18 Baker (10.1016/j.cam.2009.07.036_b17) 1981 Killingbeck (10.1016/j.cam.2009.07.036_b4) 1987; 20 Ravi Kanth (10.1016/j.cam.2009.07.036_b18) 2003; 146 Gustafsson (10.1016/j.cam.2009.07.036_b6) 1973; 21 Kumar (10.1016/j.cam.2009.07.036_b11) 2009; 40 Weinitschke (10.1016/j.cam.2009.07.036_b2) 1958; 38 Fuchs (10.1016/j.cam.2009.07.036_b13) 1905; 141 Jamet (10.1016/j.cam.2009.07.036_b5) 1970; 14 Coddington (10.1016/j.cam.2009.07.036_b14) 1955 Rutishauser (10.1016/j.cam.2009.07.036_b15) 1957 Schneider (10.1016/j.cam.2009.07.036_b1) 1979; 23 |
| References_xml | – volume: 141 start-page: 555 year: 1905 end-page: 558 ident: b13 article-title: Sur quelques équations differentielles linéaires du second ordre publication-title: C. R. Acad. Sci. – volume: 25 start-page: 427 year: 1975 end-page: 432 ident: b9 article-title: On the collocation method for singular two point boundary value problems publication-title: Numer. Math. – volume: 18 start-page: 2141 year: 1985 end-page: 2149 ident: b3 article-title: Efficient solution of differential equations by analytic continuation publication-title: J. Phys. A – year: 1955 ident: b14 article-title: Theory of Ordinary Differential Equations – volume: 38 start-page: 209 year: 1958 end-page: 231 ident: b2 article-title: On the stability, problem for shallow spherical shells publication-title: J. Math. Phys. – year: 1981 ident: b17 article-title: Padé approximants – volume: 160 start-page: 851 year: 2005 end-page: 863 ident: b10 article-title: Numerical solution of singular boundary value problems via Chebyshev polynomial and B-spline publication-title: Appl. Math. Comput. – volume: 23 start-page: 1401 year: 1979 end-page: 1606 ident: b1 article-title: A similarity solution for combined forced and free convection flow over a horizontal plate publication-title: Int. J. Heat Mass Transfer – year: 1957 ident: b15 article-title: Der Quotienten-Differenzen Algorithmus Mitteilungen Institut für angewandte Mathematik (ETH) – volume: 13 start-page: 379 year: 1974 end-page: 384 ident: b8 article-title: A note on the numerical solution of some singular second order differential equations publication-title: J. Inst. Math. Appl. – volume: 14 start-page: 355 year: 1970 end-page: 378 ident: b5 article-title: On the convergence of finite difference approximations to one dimensional singular boundary value problems publication-title: Numer. Math. – volume: vol. I year: 1974 ident: b12 publication-title: Applied and Computational Complex Analysis – volume: 21 start-page: 328 year: 1973 end-page: 344 ident: b6 article-title: A numerical method for solving singular boundary value problems publication-title: Numer. Math. – volume: 20 start-page: 1411 year: 1987 end-page: 1417 ident: b4 article-title: Shooting methods for the Schrodinger equation publication-title: J. Phys. A: Math. Gen. – reference: H. Allouche, A. Cuyt, Reliable pole detection using a deflated qd-algorithm: When Bernoulli, Hadamard and Rutishauser cooperate, Numer. Math. (in press) – volume: 75 start-page: 113 year: 2007 end-page: 125 ident: b7 article-title: Approximate solution of linear ordinary differential equations with variable coefficients publication-title: Math. Comput. Simul. – volume: 40 start-page: 288 year: 2009 end-page: 297 ident: b11 article-title: A collection of computational techniques for solving singular boundary-value problems publication-title: Adv. Eng. Softw. – volume: 156 start-page: 249 year: 2004 end-page: 259 ident: b19 article-title: Cubic spline for solving singular two-point boundary value problems publication-title: Appl. Math. Comput. – volume: 146 start-page: 691 year: 2003 end-page: 700 ident: b18 article-title: A numerical method for singular two point boundary value problems via Chebyshev economization publication-title: Appl. Math. Comput. – volume: 156 start-page: 249 year: 2004 ident: 10.1016/j.cam.2009.07.036_b19 article-title: Cubic spline for solving singular two-point boundary value problems publication-title: Appl. Math. Comput. doi: 10.1016/j.amc.2003.07.020 – volume: 13 start-page: 379 year: 1974 ident: 10.1016/j.cam.2009.07.036_b8 article-title: A note on the numerical solution of some singular second order differential equations publication-title: J. Inst. Math. Appl. doi: 10.1093/imamat/13.3.379 – volume: 141 start-page: 555 year: 1905 ident: 10.1016/j.cam.2009.07.036_b13 article-title: Sur quelques équations differentielles linéaires du second ordre publication-title: C. R. Acad. Sci. – volume: 14 start-page: 355 year: 1970 ident: 10.1016/j.cam.2009.07.036_b5 article-title: On the convergence of finite difference approximations to one dimensional singular boundary value problems publication-title: Numer. Math. doi: 10.1007/BF02165591 – volume: 40 start-page: 288 year: 2009 ident: 10.1016/j.cam.2009.07.036_b11 article-title: A collection of computational techniques for solving singular boundary-value problems publication-title: Adv. Eng. Softw. doi: 10.1016/j.advengsoft.2008.04.010 – year: 1981 ident: 10.1016/j.cam.2009.07.036_b17 – volume: 75 start-page: 113 year: 2007 ident: 10.1016/j.cam.2009.07.036_b7 article-title: Approximate solution of linear ordinary differential equations with variable coefficients publication-title: Math. Comput. Simul. doi: 10.1016/j.matcom.2006.09.006 – volume: 21 start-page: 328 year: 1973 ident: 10.1016/j.cam.2009.07.036_b6 article-title: A numerical method for solving singular boundary value problems publication-title: Numer. Math. doi: 10.1007/BF01436387 – volume: 25 start-page: 427 year: 1975 ident: 10.1016/j.cam.2009.07.036_b9 article-title: On the collocation method for singular two point boundary value problems publication-title: Numer. Math. doi: 10.1007/BF01396339 – volume: 38 start-page: 209 year: 1958 ident: 10.1016/j.cam.2009.07.036_b2 article-title: On the stability, problem for shallow spherical shells publication-title: J. Math. Phys. doi: 10.1002/sapm1959381209 – volume: 18 start-page: 2141 year: 1985 ident: 10.1016/j.cam.2009.07.036_b3 article-title: Efficient solution of differential equations by analytic continuation publication-title: J. Phys. A doi: 10.1088/0305-4470/18/12/011 – volume: 160 start-page: 851 year: 2005 ident: 10.1016/j.cam.2009.07.036_b10 article-title: Numerical solution of singular boundary value problems via Chebyshev polynomial and B-spline publication-title: Appl. Math. Comput. doi: 10.1016/j.amc.2003.12.004 – volume: 146 start-page: 691 year: 2003 ident: 10.1016/j.cam.2009.07.036_b18 article-title: A numerical method for singular two point boundary value problems via Chebyshev economization publication-title: Appl. Math. Comput. doi: 10.1016/S0096-3003(02)00613-6 – volume: 23 start-page: 1401 year: 1979 ident: 10.1016/j.cam.2009.07.036_b1 article-title: A similarity solution for combined forced and free convection flow over a horizontal plate publication-title: Int. J. Heat Mass Transfer doi: 10.1016/0017-9310(79)90202-3 – year: 1957 ident: 10.1016/j.cam.2009.07.036_b15 – ident: 10.1016/j.cam.2009.07.036_b16 – volume: vol. I year: 1974 ident: 10.1016/j.cam.2009.07.036_b12 – year: 1955 ident: 10.1016/j.cam.2009.07.036_b14 – volume: 20 start-page: 1411 year: 1987 ident: 10.1016/j.cam.2009.07.036_b4 article-title: Shooting methods for the Schrodinger equation publication-title: J. Phys. A: Math. Gen. doi: 10.1088/0305-4470/20/6/024 |
| SSID | ssj0006914 |
| Score | 1.9094577 |
| Snippet | In this paper, we present a method using qd-algorithm combined with finite difference method for numerically solving singular boundary value problems for... |
| SourceID | proquest pascalfrancis crossref elsevier |
| SourceType | Aggregation Database Index Database Enrichment Source Publisher |
| StartPage | 420 |
| SubjectTerms | Boundary value problems Degenerate problems Exact sciences and technology Finite difference scheme Formally orthogonal Hadamard polynomials Fröbenius method Mathematical analysis Mathematics Numerical analysis Numerical analysis. Scientific computation Ordinary differential equations Partial differential equations, boundary value problems Partial differential equations, initial value problems and time-dependant initial-boundary value problems Pole detection qd-Algorithm Sciences and techniques of general use Singularity |
| Title | Numerical solution of singular regular boundary value problems by pole detection with qd-algorithm |
| URI | https://dx.doi.org/10.1016/j.cam.2009.07.036 https://www.proquest.com/docview/34785815 |
| Volume | 233 |
| WOSCitedRecordID | wos000270619900031&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: 1879-1778 dateEnd: 20180131 omitProxy: false ssIdentifier: ssj0006914 issn: 0377-0427 databaseCode: AIEXJ dateStart: 19950220 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1db9MwFLXKxgMIIT5F-Rh-4IkpU-rYsf1YoSFAUCExpL5FseOwTWlS0nba_gC_m2s7TrtVmwCJlzSK4jrNOfW9vva9B6E3Ii7BLqs0YnBDRDXhkUq5XeRlBdOCG1k41ZLPfDIR06n8Ohj8CrkwZxWva3F-Luf_FWq4BmDb1Nm_gLv_UrgA5wA6HAF2OP4R8JOVX4Sp9kM_1iG0IQG347Q1_lM5PaX2Yt-W-7bZUk5YZmHd0XnjsqmWxsuIu1DtzyLKqx9NC-ezaxxa7QQiQnDRFYHtXNxZXxu29-DHVdWsgDDO9B2s4-LtcZs3qxOfBHYpJCFtbp5PyvRxsq1cGZ-fxXlklT285fHDreDQmHsRnzAeE18ZoyMe2RhdKYk3DDX1lVO2bIAPR5zC_H7W1SPlB3Fypd62s-Df7DPZR4qlk95ObqFdwpmE0XF3_PFw-qm36an0VeLDbwjr426n4JWOrvNw7s3zBYBfesGULdvvHJqjB-h-BxweewY9RANTP0J3v6yheoxUzyUcuISbEgcu4Y5LOHAJOy7hwCWsLrDlEu65hC2X8CaXnqDv7w-P3n2IOlGOSCdMLGE2lsq0LPx6qyFpYUpGyoSlSuemyCXMyIWizBhGmOK6pDwmWpZW5EmYOOfJU7RTN7V5hrBWYFFKkhieCFqYEbQfKWqIpsZwTfIhisOLzHRXsd4Kp1RZ2Jp4msG7t0qqMot5Bu9-iN72Tea-XMtNN9OATtb5m96PzIBKNzXbu4Rk3xEYf2HLLw3R6wBtBoO1XYHLa9OsFllCuWBixJ7_W88v0J313-0l2lm2K_MK3dZny5NFu9dx9jdM377G |
| 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=Numerical+solution+of+singular+regular+boundary+value+problems+by+pole+detection+with+qd-algorithm&rft.jtitle=Journal+of+computational+and+applied+mathematics&rft.au=Allouche%2C+H.&rft.au=Marhraoui%2C+N.&rft.date=2009-11-15&rft.pub=Elsevier+B.V&rft.issn=0377-0427&rft.eissn=1879-1778&rft.volume=233&rft.issue=2&rft.spage=420&rft.epage=436&rft_id=info:doi/10.1016%2Fj.cam.2009.07.036&rft.externalDocID=S0377042709004403 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0377-0427&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0377-0427&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0377-0427&client=summon |