{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,3,31]],"date-time":"2023-03-31T23:40:42Z","timestamp":1680306042203},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2016,4,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>The aim of this paper is to approximate the solution of a class of\nintegral equations of the third kind on an unbounded domain. For\ncomputing such approximation, the collocation method based on the\ngeneralized Laguerre abscissas is considered. In this method, the\nunknown function is interpolated at the nodal points\n<jats:inline-formula id=\"eq1_w2aab2b8b5b1b7b1aab1c13b1b1Aa\">\n                     <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/cmam-2015-0038_4f825ae980e3426659dadf7cb16835e8.png\" \/>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:msubsup>\n                              <m:mrow>\n                                 <m:mo>{<\/m:mo>\n                                 <m:msub>\n                                    <m:mi>t<\/m:mi>\n                                    <m:mi>i<\/m:mi>\n                                 <\/m:msub>\n                                 <m:mo>}<\/m:mo>\n                              <\/m:mrow>\n                              <m:mrow>\n                                 <m:mi>i<\/m:mi>\n                                 <m:mo>=<\/m:mo>\n                                 <m:mn>1<\/m:mn>\n                              <\/m:mrow>\n                              <m:mrow>\n                                 <m:mi>n<\/m:mi>\n                                 <m:mo>+<\/m:mo>\n                                 <m:mn>1<\/m:mn>\n                              <\/m:mrow>\n                           <\/m:msubsup>\n                        <\/m:math>\n                        <jats:tex-math>${\\lbrace t_i\\rbrace _{i=1}^{n+1}}$<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula>, where <jats:inline-formula id=\"eq2_w2aab2b8b5b1b7b1aab1c13b1b3Aa\">\n                     <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/cmam-2015-0038_c012ecd58ada194a49722ebb070019c7.png\" \/>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:msubsup>\n                              <m:mrow>\n                                 <m:mo>{<\/m:mo>\n                                 <m:msub>\n                                    <m:mi>t<\/m:mi>\n                                    <m:mi>i<\/m:mi>\n                                 <\/m:msub>\n                                 <m:mo>}<\/m:mo>\n                              <\/m:mrow>\n                              <m:mrow>\n                                 <m:mi>i<\/m:mi>\n                                 <m:mo>=<\/m:mo>\n                                 <m:mn>1<\/m:mn>\n                              <\/m:mrow>\n                              <m:mi>n<\/m:mi>\n                           <\/m:msubsup>\n                        <\/m:math>\n                        <jats:tex-math>${\\lbrace t_i\\rbrace _{i=1}^{n}}$<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula> are the zeros of\ngeneralized Laguerre polynomials and <jats:inline-formula id=\"eq3_w2aab2b8b5b1b7b1aab1c13b1b5Aa\">\n                     <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/cmam-2015-0038_4b29a52defe065ba7aa3de3c637bc1f7.png\" \/>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:mrow>\n                              <m:msub>\n                                 <m:mi>t<\/m:mi>\n                                 <m:mrow>\n                                    <m:mi>n<\/m:mi>\n                                    <m:mo>+<\/m:mo>\n                                    <m:mn>1<\/m:mn>\n                                 <\/m:mrow>\n                              <\/m:msub>\n                              <m:mo>=<\/m:mo>\n                              <m:mn>4<\/m:mn>\n                              <m:mi>n<\/m:mi>\n                           <\/m:mrow>\n                        <\/m:math>\n                        <jats:tex-math>${t_{n+1}=4n}$<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula>. Then, the given\nequation is transformed to the Fredholm integral equation of the\nsecond kind. In the sequel, according to the integration interval,\nwe apply the Gauss\u2013Laguerre collocation method on the interval\n<jats:inline-formula id=\"eq4_w2aab2b8b5b1b7b1aab1c13b1b7Aa\">\n                     <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/cmam-2015-0038_fdc0de09c8275e091194fba196f9436a.png\" \/>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:mrow>\n                              <m:mo>[<\/m:mo>\n                              <m:mn>0<\/m:mn>\n                              <m:mo>,<\/m:mo>\n                              <m:mi>\u221e<\/m:mi>\n                              <m:mo>)<\/m:mo>\n                           <\/m:mrow>\n                        <\/m:math>\n                        <jats:tex-math>${[0,\\infty )}$<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula> by using the given nodal points. Therefore, the\nsolution of the third kind integral equation is reduced to the\nsolution of a system of linear equations. Convergence analysis of\nthe method in some Sobolev-type space is studied. Illustrative\nexamples are included to demonstrate the validity and applicability\nof the technique.<\/jats:p>","DOI":"10.1515\/cmam-2015-0038","type":"journal-article","created":{"date-parts":[[2016,4,4]],"date-time":"2016-04-04T17:39:25Z","timestamp":1459791565000},"page":"245-256","source":"Crossref","is-referenced-by-count":0,"title":["The Laguerre Collocation Method for Third Kind Integral Equations\non Unbounded Domains"],"prefix":"10.1515","volume":"16","author":[{"given":"Farideh","family":"Ghoreishi","sequence":"first","affiliation":[{"name":"Faculty of Mathematics, K. N. Toosi University of Technology, Tehran, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Elena","family":"Farahbakhsh-Tooli","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Sharif University of Technology, Tehran, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2016,1,14]]},"container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/16\/2\/article-p245.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2015-0038\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2015-0038\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,31]],"date-time":"2023-03-31T22:59:47Z","timestamp":1680303587000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2015-0038\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,1,14]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2016,2,20]]},"published-print":{"date-parts":[[2016,4,1]]}},"alternative-id":["10.1515\/cmam-2015-0038"],"URL":"https:\/\/doi.org\/10.1515\/cmam-2015-0038","relation":{},"ISSN":["1609-4840","1609-9389"],"issn-type":[{"value":"1609-4840","type":"print"},{"value":"1609-9389","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,1,14]]}}}