{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,4,15]],"date-time":"2025-04-15T04:00:39Z","timestamp":1744689639430,"version":"3.40.4"},"reference-count":19,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2025,3,18]],"date-time":"2025-03-18T00:00:00Z","timestamp":1742256000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,3,18]],"date-time":"2025-03-18T00:00:00Z","timestamp":1742256000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comp. Appl. Math."],"published-print":{"date-parts":[[2025,6]]},"DOI":"10.1007\/s40314-025-03157-3","type":"journal-article","created":{"date-parts":[[2025,3,18]],"date-time":"2025-03-18T00:39:21Z","timestamp":1742258361000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A capable collocation method for solving a class of nonlinear Volterra integral equations of the third kind"],"prefix":"10.1007","volume":"44","author":[{"given":"Rohollah Ghaedi","family":"Ghalini","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1236-1052","authenticated-orcid":false,"given":"Hojatollah Laeli","family":"Dastjerdi","sequence":"additional","affiliation":[]},{"given":"Esmail","family":"Hesameddini","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,3,18]]},"reference":[{"key":"3157_CR1","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511543234","volume-title":"Collocation methods for Volterra integral and related functional equations","author":"H Brunner","year":"2004","unstructured":"Brunner H (2004) Collocation methods for Volterra integral and related functional equations. Cambridge University Press, Cambridge"},{"key":"3157_CR2","doi-asserted-by":"publisher","DOI":"10.1017\/9781316162491","volume-title":"Volterra integral equations: an introduction to theory and applications","author":"H Brunner","year":"2017","unstructured":"Brunner H (2017) Volterra integral equations: an introduction to theory and applications. Cambridge University Press, Cambridge"},{"key":"3157_CR3","doi-asserted-by":"crossref","unstructured":"Canuto C, Hussaini MY, Quarteroni A, Zang TA (2006) Spectral methods, fundamentals in single domains. Springer, Berlin","DOI":"10.1007\/978-3-540-30726-6"},{"key":"3157_CR4","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1090\/S0025-5718-09-02269-8","volume":"79","author":"Y Chen","year":"2010","unstructured":"Chen Y, Tang T (2010) Convergence analysis of the Jacobi Spectral Collocation Methods for Volterra Integral equations with a weakly singular kernel. J Math Comp 79:147\u2013167","journal-title":"J Math Comp"},{"key":"3157_CR5","doi-asserted-by":"publisher","first-page":"88","DOI":"10.1016\/j.cam.2013.12.002","volume":"263","author":"P Das","year":"2014","unstructured":"Das P, Sahani MM, Nelakanti G (2014) Legendre spectral projection methods for Urysohn integral equations. J Comput Appl Math 263:88\u2013102","journal-title":"J Comput Appl Math"},{"key":"3157_CR6","first-page":"393","volume":"11","author":"GC Evans","year":"1910","unstructured":"Evans GC (1910) Volterra\u2019s integral equation of the second kind with discontinuous kernel. Trans Am Math Soc 11:393\u2013413","journal-title":"Trans Am Math Soc"},{"key":"3157_CR7","doi-asserted-by":"publisher","first-page":"115","DOI":"10.1016\/j.cam.2012.10.033","volume":"244","author":"Y Jiang","year":"2013","unstructured":"Jiang Y, Ma J (2013) Spectral collocation methods for Volterra integro-differential equations with noncompact kernels. J Comput Appl Math 244:115\u2013124","journal-title":"J Comput Appl Math"},{"key":"3157_CR8","doi-asserted-by":"crossref","unstructured":"Kherchouche K, Bellour A, Lima P (2023) Numerical solution of nonlinear third kind Volterra integral equations using an iterative collocation method. Int J Comput Math 14(just-accepted):1","DOI":"10.1080\/00207160.2023.2260007"},{"key":"3157_CR9","first-page":"325","volume":"27","author":"S Seyed Allaei","year":"2015","unstructured":"Seyed Allaei S, Yang ZW, Brunner H (2015) Existence, uniqueness and regularity of solutions for a class of third-kind Volterra integral equations. J Integral Equ. Appl 27:325\u2013342","journal-title":"J Integral Equ. Appl"},{"key":"3157_CR10","doi-asserted-by":"publisher","first-page":"673","DOI":"10.1007\/s10915-016-0213-x","volume":"69","author":"S Seyed Allaei","year":"2016","unstructured":"Seyed Allaei S, Diogo T, Rebelo M (2016) The Jacobi Collocation method for a class of nonlinear volterra integral equations with weakly singular kernel. J Sci Comput 69:673\u2013695","journal-title":"J Sci Comput"},{"key":"3157_CR11","first-page":"1104","volume":"37","author":"S Seyed Allaei","year":"2017","unstructured":"Seyed Allaei S, Yang ZW, Brunner H (2017) Collocation methods for third-kind VIEs. IMA J Numer Anal 37:1104\u20131124","journal-title":"IMA J Numer Anal"},{"key":"3157_CR12","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s40314-019-0947-9","volume":"38","author":"F Shayanfard","year":"2019","unstructured":"Shayanfard F, Laeli Dastjerdi H, Maalek Ghaini F (2019) A numerical method for solving Volterra integral equations of the third kind by multistep collocation method. Comput Appl Math 38:1\u201313","journal-title":"Comput Appl Math"},{"key":"3157_CR13","series-title":"Analysis and Applications","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-71041-7","volume-title":"Spectral Methods Algorithms","author":"J Shen","year":"2011","unstructured":"Shen J, Tang T, Wang L (2011) Spectral Methods Algorithms. Analysis and Applications. Springer, Berlin"},{"key":"3157_CR14","doi-asserted-by":"crossref","unstructured":"Song H, Yang Z, Brunner H (2019) Analysis of collocation methods for nonlinear Volterra integral equations of the third kind. Calcolo 56","DOI":"10.1007\/s10092-019-0304-9"},{"key":"3157_CR15","volume":"388","author":"H Song","year":"2020","unstructured":"Song H, Xiao Y, Chen M (2020) Collocation methods for third-kind Volterra integral equations with proportional delays. Appl Math Comput 388:125509","journal-title":"Appl Math Comput"},{"key":"3157_CR16","first-page":"825","volume":"26","author":"T Tang","year":"2008","unstructured":"Tang T, Xu X, Chen J (2008) On spectral methods for Volterra type integral equations and the convergence analysis. J Comput Math 26:825\u2013837","journal-title":"J Comput Math"},{"issue":"4","key":"3157_CR17","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/0041-5553(67)90140-1","volume":"7","author":"G Vainikko","year":"1967","unstructured":"Vainikko G (1967) A perturbed Galerkin method and the general theory of approximate methods for nonlinear equations. USSR Comput Math Math Phys 7(4):1\u201341","journal-title":"USSR Comput Math Math Phys"},{"key":"3157_CR18","doi-asserted-by":"publisher","first-page":"1145","DOI":"10.1080\/01630560903393188","volume":"30","author":"G Vainikko","year":"2009","unstructured":"Vainikko G (2009) Cordial Volterra integral equation 1. Numer Funct Anal Optim 30:1145\u20131172","journal-title":"Numer Funct Anal Optim"},{"key":"3157_CR19","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1080\/01630563.2010.526412","volume":"32","author":"G Vainikko","year":"2011","unstructured":"Vainikko G (2011) Spline collocation-interpolation method for linear and nonlinear cordial Volterra integral equations. Numer Funct Anal Optim 32:83\u2013109","journal-title":"Numer Funct Anal Optim"}],"container-title":["Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-025-03157-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40314-025-03157-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-025-03157-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,14]],"date-time":"2025-04-14T04:26:49Z","timestamp":1744604809000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40314-025-03157-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,3,18]]},"references-count":19,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2025,6]]}},"alternative-id":["3157"],"URL":"https:\/\/doi.org\/10.1007\/s40314-025-03157-3","relation":{},"ISSN":["2238-3603","1807-0302"],"issn-type":[{"type":"print","value":"2238-3603"},{"type":"electronic","value":"1807-0302"}],"subject":[],"published":{"date-parts":[[2025,3,18]]},"assertion":[{"value":"22 April 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 January 2025","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 February 2025","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 March 2025","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"193"}}