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The method is based on (i) improving the boundary behavior of the kernel with the help of a change of variables, and (ii) the product integration using quasi-interpolation by smooth splines of order m.<\/jats:p>","DOI":"10.1137\/070693308","type":"journal-article","created":{"date-parts":[[2008,4,16]],"date-time":"2008-04-16T18:05:23Z","timestamp":1208369123000},"page":"1799-1820","source":"Crossref","is-referenced-by-count":41,"title":["A Spline Product Quasi-interpolation Method for Weakly Singular Fredholm Integral Equations"],"prefix":"10.1137","volume":"46","author":[{"given":"Eero","family":"Vainikko","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Gennadi","family":"Vainikko","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2008,4,16]]},"reference":[{"key":"R1","unstructured":"P. M. 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Vainikko,\n                      A product quasi-interpolation method for weakly singular Volterra integral equations\n                      , in Numerical Analysis and Applied Mathematics, Vol. 936, T. E. Simos, ed., AIP Conference Proceedings, American Institute of Physics, Melville, NY, 2007, pp. 570\u2013573.","DOI":"10.1063\/1.2790209"},{"key":"R18","unstructured":"G. Vainikko,\n                      Funktionalanalysis der Diskretisierungsmethoden\n                      , Teubner, Leipzig, 1976."},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.3176\/phys.math.2004.2.08"},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1216\/jiea\/1181075312"},{"key":"R21","first-page":"523","volume":"4","author":"Vainikko G.","year":"2006","journal-title":"WSEAS Trans. Math."},{"key":"R22","unstructured":"G. Vainikko,\n                      Error estimates for the cardinal spline interpolation\n                      , Z. Anal. Anwend., to appear."}],"container-title":["SIAM Journal on Numerical Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/070693308","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T15:14:02Z","timestamp":1787325242000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/070693308"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,1]]},"references-count":22,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2008,1]]}},"alternative-id":["10.1137\/070693308"],"URL":"https:\/\/doi.org\/10.1137\/070693308","relation":{},"ISSN":["0036-1429","1095-7170"],"issn-type":[{"value":"0036-1429","type":"print"},{"value":"1095-7170","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,1]]}}}