{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,8]],"date-time":"2025-12-08T21:55:00Z","timestamp":1765230900070,"version":"3.41.0"},"reference-count":13,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2008,7,1]],"date-time":"2008-07-01T00:00:00Z","timestamp":1214870400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Math. Softw."],"published-print":{"date-parts":[[2008,7,15]]},"abstract":"<jats:p>\n            We present here the algorithms and user interface of a\n            <jats:sc>Matlab<\/jats:sc>\n            program, Fie, that solves numerically Fredholm integral equations of the second kind on an interval [\n            <jats:italic>a<\/jats:italic>\n            ,\n            <jats:italic>b<\/jats:italic>\n            ] to a specified, modest accuracy. The kernel function\n            <jats:italic>K<\/jats:italic>\n            (\n            <jats:italic>s<\/jats:italic>\n            ,\n            <jats:italic>t<\/jats:italic>\n            ) is moderately smooth on [\n            <jats:italic>a<\/jats:italic>\n            ,\n            <jats:italic>b<\/jats:italic>\n            ] \u00d7[\n            <jats:italic>a<\/jats:italic>\n            ,\n            <jats:italic>b<\/jats:italic>\n            ] except possibly across the diagonal\n            <jats:italic>s<\/jats:italic>\n            \u2009=\u2009\n            <jats:italic>t<\/jats:italic>\n            . If the interval is finite, provides for kernel functions that behave in a variety of ways across the diagonal, that is,\n            <jats:italic>K<\/jats:italic>\n            (\n            <jats:italic>s<\/jats:italic>\n            ,\n            <jats:italic>t<\/jats:italic>\n            ) may be smooth, have a discontinuity in a low-order derivative, have a logarithmic singularity, or have an algebraic singularity. Fie also solves a large class of integral equations with moderately smooth kernel function on [0,\u2009\u221e\u2009).\n          <\/jats:p>","DOI":"10.1145\/1377596.1377601","type":"journal-article","created":{"date-parts":[[2008,7,22]],"date-time":"2008-07-22T13:04:05Z","timestamp":1216731845000},"page":"1-20","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":54,"title":["Algorithm 876"],"prefix":"10.1145","volume":"34","author":[{"given":"Kendall E.","family":"Atkinson","sequence":"first","affiliation":[{"name":"University of Iowa"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lawrence F.","family":"Shampine","sequence":"additional","affiliation":[{"name":"Southern Methodist University, Dallas"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2008,7]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1137\/0704029"},{"volume-title":"A Survey of Numerical Methods for the Solution of Fredholm Integral Equations of the Second Kind","author":"Atkinson K.","key":"e_1_2_2_2_1","unstructured":"Atkinson , K. 1976a. A Survey of Numerical Methods for the Solution of Fredholm Integral Equations of the Second Kind . SIAM , Philadelphia, PA . Atkinson, K. 1976a. A Survey of Numerical Methods for the Solution of Fredholm Integral Equations of the Second Kind. SIAM, Philadelphia, PA."},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/355681.355686"},{"volume-title":"The Numerical Solution of Integral Equations of the Second Kind","author":"Atkinson K.","key":"e_1_2_2_4_1","unstructured":"Atkinson , K. 1997. The Numerical Solution of Integral Equations of the Second Kind . Cambridge University Press , Cambridge, UK . Atkinson, K. 1997. The Numerical Solution of Integral Equations of the Second Kind. Cambridge University Press, Cambridge, UK."},{"key":"e_1_2_2_5_1","doi-asserted-by":"crossref","unstructured":"Atkinson K. and Han W. 2005. Theoretical Numerical Analysis: A Functional Analysis Framework 2nd Ed. Springer-Verlag Berlin Germany. Atkinson K. and Han W. 2005. Theoretical Numerical Analysis: A Functional Analysis Framework 2 nd Ed. Springer-Verlag Berlin Germany.","DOI":"10.1007\/978-0-387-28769-0"},{"key":"e_1_2_2_6_1","doi-asserted-by":"publisher","DOI":"10.1016\/0377-0427(84)90065-7"},{"key":"e_1_2_2_7_1","doi-asserted-by":"publisher","DOI":"10.1093\/comjnl\/12.3.282"},{"volume-title":"Numerical Solution of Ordinary and Partial Differential Equations","author":"Fox L.","key":"e_1_2_2_8_1","unstructured":"Fox , L. 1962. Numerical Solution of Ordinary and Partial Differential Equations . Pergamon Press , London, UK . Fox, L. 1962. Numerical Solution of Ordinary and Partial Differential Equations. Pergamon Press, London, UK."},{"key":"e_1_2_2_9_1","doi-asserted-by":"publisher","DOI":"10.1063\/1.1746947"},{"key":"e_1_2_2_10_1","doi-asserted-by":"publisher","DOI":"10.1093\/qjmam\/2.4.428"},{"volume-title":"The MathWorks","author":"Matlab","key":"e_1_2_2_11_1","unstructured":"Matlab . The MathWorks , Inc., 3 Apple Hill Drive, Natick, MA 01760. Matlab. The MathWorks, Inc., 3 Apple Hill Drive, Natick, MA 01760."},{"key":"e_1_2_2_12_1","unstructured":"Mikhlin S. G. and Smolitskiy K. L. 1967. Approximate Methods for Solution of Differential and Integral Equations. Elsevier London UK. Mikhlin S. G. and Smolitskiy K. L. 1967. Approximate Methods for Solution of Differential and Integral Equations . Elsevier London UK."},{"key":"e_1_2_2_13_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1981-0606510-2"}],"container-title":["ACM Transactions on Mathematical Software"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1377596.1377601","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1377596.1377601","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T13:57:56Z","timestamp":1750255076000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1377596.1377601"}},"subtitle":["Solving Fredholm Integral Equations of the Second Kind in Matlab"],"short-title":[],"issued":{"date-parts":[[2008,7]]},"references-count":13,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2008,7,15]]}},"alternative-id":["10.1145\/1377596.1377601"],"URL":"https:\/\/doi.org\/10.1145\/1377596.1377601","relation":{},"ISSN":["0098-3500","1557-7295"],"issn-type":[{"type":"print","value":"0098-3500"},{"type":"electronic","value":"1557-7295"}],"subject":[],"published":{"date-parts":[[2008,7]]},"assertion":[{"value":"2006-12-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2007-07-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2008-07-01","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}