{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T12:54:58Z","timestamp":1740142498826,"version":"3.37.3"},"reference-count":36,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2021,8,18]],"date-time":"2021-08-18T00:00:00Z","timestamp":1629244800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,8,18]],"date-time":"2021-08-18T00:00:00Z","timestamp":1629244800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comp. Appl. Math."],"published-print":{"date-parts":[[2021,9]]},"DOI":"10.1007\/s40314-021-01610-7","type":"journal-article","created":{"date-parts":[[2021,8,18]],"date-time":"2021-08-18T16:02:47Z","timestamp":1629302567000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A spectral collocation matrix method for solving linear Fredholm integro-differential\u2013difference equations"],"prefix":"10.1007","volume":"40","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4142-5633","authenticated-orcid":false,"given":"Yal\u00e7\u0131n","family":"\u00d6zt\u00fcrk","sequence":"first","affiliation":[]},{"given":"At\u0131l\u0131m Ilker","family":"Demir","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,8,18]]},"reference":[{"key":"1610_CR1","first-page":"Article ID 7157","volume":"2013","author":"WM Abd-Elhameed","year":"2013","unstructured":"Abd-Elhameed WM, Doha EH, Youssri YH (2013) New spectral second kind Chebyshev wavelets algorithm for solving linear and nonlinear second-order differential equations involving singular and Bratu type equations. Abstr Appl Anal 2013:Article ID 715756","journal-title":"Abstr Appl Anal"},{"key":"1610_CR2","doi-asserted-by":"publisher","first-page":"494","DOI":"10.1186\/s13662-020-02951-z","volume":"2020","author":"KK Ali","year":"2020","unstructured":"Ali KK, Abd El Salam MA, Mohammed EMH, Samet B, Kumar S, Osman MS (2020) Numerical solution for generalized nonlinear fractional integro-differential equations with linear functional arguments using Chebyshev series. Adv Differ Equ 2020:494","journal-title":"Adv Differ Equ"},{"key":"1610_CR3","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/j.amc.2015.09.085","volume":"273","author":"MA Balci","year":"2016","unstructured":"Balci MA, Sezer M (2016) Hybrid Euler\u2013Taylor matrix method for solving of generalize linear Fredholm integro-differential difference equations. Appl Math Comput 273:33\u201341","journal-title":"Appl Math Comput"},{"issue":"10","key":"1610_CR4","doi-asserted-by":"publisher","first-page":"2100","DOI":"10.1080\/00207160.2017.1366458","volume":"95","author":"GG Bicer","year":"2018","unstructured":"Bicer GG, Ozturk Y, Gulsu M (2018) Numerical approach for solving linear Fredholm integro-differential equation with piecewise intervals by Bernoulli polynomials. Int J Comput Math 95(10):2100\u20132111","journal-title":"Int J Comput Math"},{"key":"1610_CR5","doi-asserted-by":"crossref","first-page":"910","DOI":"10.1016\/j.amc.2005.05.019","volume":"174","author":"I Celik","year":"2006","unstructured":"Celik I (2006) Collocation method and residual correction using Chebyshev series. Appl Math Comput 174:910\u2013920","journal-title":"Appl Math Comput"},{"key":"1610_CR6","doi-asserted-by":"publisher","first-page":"ArticleID 31","DOI":"10.1007\/s40314-021-01424-7","volume":"40","author":"S Chakraborty","year":"2021","unstructured":"Chakraborty S, Nelakanti G (2021) Approximation methods for system of nonlinear Fredholm\u2013Hammerstein integral equations. Comput Appl Math 40:ArticleID 31","journal-title":"Comput Appl Math"},{"issue":"1","key":"1610_CR7","doi-asserted-by":"publisher","first-page":"123","DOI":"10.1080\/00207160701405436","volume":"85","author":"M Dehghan","year":"2008","unstructured":"Dehghan M, Saadatmandi A (2008) Chebyshev finite difference method for Fredholm integro-differential equation. Int J Comput Math 85(1):123\u2013130","journal-title":"Int J Comput Math"},{"key":"1610_CR8","doi-asserted-by":"publisher","first-page":"113","DOI":"10.1016\/j.newast.2013.03.002","volume":"23\u201324","author":"EH Doha","year":"2013","unstructured":"Doha EH, Abd-Elhameed WM, Youssri YH (2013) Second kind Chebyshev operational matrix algorithm for solving differential equations of Lane\u2013Emden type. New Astron 23\u201324:113\u2013117","journal-title":"New Astron"},{"key":"1610_CR9","doi-asserted-by":"publisher","first-page":"720","DOI":"10.1016\/j.jfranklin.2006.07.003","volume":"343","author":"M Gulsu","year":"2006","unstructured":"Gulsu M, Sezer M (2006) Approximations to the solution of linear Fredholm integro-differential-difference equation of high order. J Franklin Inst 343:720\u2013737","journal-title":"J Franklin Inst"},{"issue":"4","key":"1610_CR10","doi-asserted-by":"publisher","first-page":"429","DOI":"10.1080\/00207160600988342","volume":"83","author":"M Gulsu","year":"2007","unstructured":"Gulsu M, Sezer M (2007) Taylor collocation method for solution of systems of high-order linear Fredholm\u2013Volterra integro-differential equations. Int J Comput Math 83(4):429\u2013448","journal-title":"Int J Comput Math"},{"issue":"7","key":"1610_CR11","doi-asserted-by":"crossref","first-page":"2183","DOI":"10.1016\/j.amc.2010.03.054","volume":"216","author":"M Gulsu","year":"2010","unstructured":"Gulsu M, Ozturk Y, Sezer M (2010) A new collocation method for solution of mixed linear integro-differential-difference equations. Appl Math Comput 216(7):2183\u20132198","journal-title":"Appl Math Comput"},{"key":"1610_CR12","doi-asserted-by":"crossref","first-page":"4827","DOI":"10.1016\/j.amc.2010.11.044","volume":"217","author":"M Gulsu","year":"2011","unstructured":"Gulsu M, Ozturk Y, Sezer M (2011) On the solution of the Abel equation of the second kind by the shifted Chebyshev polynomials. Appl Math Comput 217:4827\u20134833","journal-title":"Appl Math Comput"},{"issue":"1","key":"1610_CR13","doi-asserted-by":"publisher","first-page":"173","DOI":"10.1080\/00207160.2015.1099633","volume":"94","author":"M Gulsu","year":"2017","unstructured":"Gulsu M, Anapali A, Ozturk Y (2017) Numerical solution the fractional Bagley\u2013Torvik equation arising in fluid mechanics. Int J Comput Math 94(1):173\u2013184","journal-title":"Int J Comput Math"},{"key":"1610_CR14","doi-asserted-by":"crossref","unstructured":"Gumgum S, Sasaneril NB, Kurkcu OK, Sezer M (2019) Lucas polynomial solution of nonlinear differential equations with variables delays. Hacet J Math Stat (in press)","DOI":"10.15672\/hujms.460975"},{"key":"1610_CR15","doi-asserted-by":"publisher","first-page":"ArticleID 68239","DOI":"10.1155\/2014\/682398","volume":"2014","author":"B Gurbuz","year":"2014","unstructured":"Gurbuz B, Sezer M, Guler C (2014) Laguerre collocation method for solving Fredholm integro-differential equations with functional arguments. J Appl Math 2014:ArticleID 682398","journal-title":"J Appl Math"},{"issue":"1","key":"1610_CR16","first-page":"114","volume":"50","author":"J Hou","year":"2020","unstructured":"Hou J, Yang C, Lv X (2020) Jacobi collocation methods for solving the fractional Bagley\u2013Torvik equation. Int J Appl Math 50(1):114\u2013120","journal-title":"Int J Appl Math"},{"key":"1610_CR17","doi-asserted-by":"publisher","first-page":"ArticleID 11253","DOI":"10.1016\/j.cam.2019.112531","volume":"368","author":"K Kant","year":"2020","unstructured":"Kant K, Nelakanti G (2020) Approximation methods for second kind weakly singular Volterra integral equations. J Comput Appl Math 368:ArticleID 112531","journal-title":"J Comput Appl Math"},{"key":"1610_CR18","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1007\/s40096-019-00314-8","volume":"14","author":"OK Kurkcu","year":"2020","unstructured":"Kurkcu OK (2020) A numerical method with a control parameter for integro-differential delay equations with state-dependent bounds via generalized Mott polynomial. Math Sci 14:43\u201352","journal-title":"Math Sci"},{"key":"1610_CR19","first-page":"113","volume":"286","author":"OK Kurkcu","year":"2021","unstructured":"Kurkcu OK, Sezer M (2021) A directly convergent numerical method based on orthoexponential polynomials for solving integro-differential-delay equations with variable coefficients and infinite boundary on half-line. J Comput Appl Math 286:113\u2013250","journal-title":"J Comput Appl Math"},{"key":"1610_CR20","doi-asserted-by":"crossref","first-page":"324","DOI":"10.1016\/j.amc.2015.12.025","volume":"276","author":"OK Kurkcu","year":"2016","unstructured":"Kurkcu OK, Aslan E, Sezer M (2016) A numerical approach with error estimation to solve general integro-differential-difference equations using Dickson polynomials. Appl Math Comput 276:324\u2013339","journal-title":"Appl Math Comput"},{"key":"1610_CR21","doi-asserted-by":"publisher","first-page":"134","DOI":"10.1016\/j.apnum.2017.06.015","volume":"121","author":"OK Kurkcu","year":"2017","unstructured":"Kurkcu OK, Aslan E, Sezer M (2017) A numerical method for solving some model problems arising in science and convergence analysis based on residual function. Appl Numer Math 121:134\u2013148","journal-title":"Appl Numer Math"},{"issue":"3","key":"1610_CR22","first-page":"396","volume":"7","author":"OK Kurkcu","year":"2019","unstructured":"Kurkcu OK, Aslan E, Sezer M (2019) A novel hybrid method for solving combined functional neutral differential equations with several delays and investigation of convergence rate via residual function. Comput Methods Differ Equ 7(3):396\u2013417","journal-title":"Comput Methods Differ Equ"},{"key":"1610_CR23","volume-title":"Theory of integro-differential equations","author":"V Lakshmikantham","year":"1993","unstructured":"Lakshmikantham V, Rao MRM (1993) Theory of integro-differential equations. Gordon and Breach Science Publishers, Switzerland"},{"key":"1610_CR24","volume-title":"Chebyshev polynomials","author":"JC Mason","year":"2003","unstructured":"Mason JC, Handscomb DC (2003) Chebyshev polynomials. Chapman and Hall\/CRC, New York"},{"key":"1610_CR25","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-08542-4","volume-title":"Mathematical biology","author":"JD Murray","year":"1993","unstructured":"Murray JD (1993) Mathematical biology, 2nd edn. Springer, New York","edition":"2"},{"key":"1610_CR26","doi-asserted-by":"crossref","first-page":"943","DOI":"10.1016\/j.amc.2015.03.024","volume":"259","author":"C Oguz","year":"2015","unstructured":"Oguz C, Sezer M (2015) Chelyshkov collocation method for a class of mixed functional integro-differential equations. Appl Math Comput 259:943\u2013954","journal-title":"Appl Math Comput"},{"key":"1610_CR27","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1007\/BF01395986","volume":"36","author":"FA Oliveira","year":"1980","unstructured":"Oliveira FA (1980) Collocation and residual correction. Numer Math 36:27\u201331","journal-title":"Numer Math"},{"issue":"1","key":"1610_CR28","doi-asserted-by":"publisher","first-page":"66","DOI":"10.11121\/ijocta.01.2017.00308","volume":"7","author":"Y Ozturk","year":"2017","unstructured":"Ozturk Y, Gulsu M (2017) Approximate solution of generalized pantograph equations with variable coefficients by operational method. Int J Optim Control Theor Appl 7(1):66\u201374","journal-title":"Int J Optim Control Theor Appl"},{"key":"1610_CR29","doi-asserted-by":"publisher","first-page":"24","DOI":"10.1140\/epjp\/i2016-16024-8","volume":"131","author":"K Parand","year":"2016","unstructured":"Parand K, Khaleqi S (2016) The rational Chebyshev of second kind collocation method for solving a class of astrophysics problems. Eur Phys J Plus 131:24","journal-title":"Eur Phys J Plus"},{"key":"1610_CR30","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139171502","volume-title":"Approximation theory and methods","author":"MJD Powel","year":"1981","unstructured":"Powel MJD (1981) Approximation theory and methods. Cambridge University Press, Cambridge"},{"key":"1610_CR31","doi-asserted-by":"publisher","first-page":"2996","DOI":"10.1016\/j.camwa.2010.02.018","volume":"59","author":"A Saadatmandi","year":"2010","unstructured":"Saadatmandi A, Dehghan M (2010) Numerical solution of the higher-order linear Fredholm integro-differential-difference equation with variable coefficients. Comput Math Appl 59:2996\u20133004","journal-title":"Comput Math Appl"},{"key":"1610_CR32","doi-asserted-by":"publisher","first-page":"381","DOI":"10.1007\/s11075-017-0320-2","volume":"77","author":"KS Sadri","year":"2018","unstructured":"Sadri KS, Amini A, Cheng C (2018) A new numerical method for delay and advanced integro-differential equations. Numer Algorithms 77:381\u2013412","journal-title":"Numer Algorithms"},{"key":"1610_CR33","doi-asserted-by":"crossref","first-page":"575","DOI":"10.1016\/j.amc.2015.06.118","volume":"268","author":"PK Sahu","year":"2015","unstructured":"Sahu PK, Ray SS (2015) Legendre spectral collocation method for Fredholm integro-differential-difference equation with variable coefficients and mixed conditions. Appl Math Comput 268:575\u2013580","journal-title":"Appl Math Comput"},{"issue":"5","key":"1610_CR34","doi-asserted-by":"publisher","first-page":"1130","DOI":"10.1002\/num.20573","volume":"7","author":"M Sezer","year":"2011","unstructured":"Sezer M, Gulsu M, Tanay B (2011) Rational Chebyshev collocation method for solving higher order linear ordinary differential equations. Numer Methods Partial Differ Equ 7(5):1130\u20131142","journal-title":"Numer Methods Partial Differ Equ"},{"key":"1610_CR35","doi-asserted-by":"publisher","first-page":"337","DOI":"10.1007\/BF00275082","volume":"4","author":"HR Thiem","year":"1977","unstructured":"Thiem HR (1977) A model for spatio spread of an epidemic. J Math Biol 4:337\u2013351","journal-title":"J Math Biol"},{"key":"1610_CR36","doi-asserted-by":"publisher","DOI":"10.1142\/3444","volume-title":"A first course in integral equations","author":"AM Wazwaz","year":"1997","unstructured":"Wazwaz AM (1997) A first course in integral equations. World Scientific, Hackensack"}],"container-title":["Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-021-01610-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40314-021-01610-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-021-01610-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,7]],"date-time":"2023-11-07T14:40:48Z","timestamp":1699368048000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40314-021-01610-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,8,18]]},"references-count":36,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2021,9]]}},"alternative-id":["1610"],"URL":"https:\/\/doi.org\/10.1007\/s40314-021-01610-7","relation":{},"ISSN":["2238-3603","1807-0302"],"issn-type":[{"type":"print","value":"2238-3603"},{"type":"electronic","value":"1807-0302"}],"subject":[],"published":{"date-parts":[[2021,8,18]]},"assertion":[{"value":"30 November 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 February 2021","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 August 2021","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 August 2021","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"218"}}