{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,7]],"date-time":"2025-10-07T12:04:48Z","timestamp":1759838688145,"version":"3.41.2"},"reference-count":7,"publisher":"Emerald","issue":"3\/4","license":[{"start":{"date-parts":[[2009,4,10]],"date-time":"2009-04-10T00:00:00Z","timestamp":1239321600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.emerald.com\/insight\/site-policies"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2009,4,10]]},"abstract":"<jats:sec><jats:title content-type=\"abstract-heading\">Purpose<\/jats:title><jats:p>The purpose of this paper is to use Alpert wavelet basis and modify the integrand function approximation coefficients to solve Fredholm\u2010Hammerstein integral equations.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Design\/methodology\/approach<\/jats:title><jats:p><jats:italic>L<\/jats:italic><jats:sup>2<\/jats:sup>[0, 1] was considered as solution space and the solution was projected to the subspaces of <jats:italic>L<\/jats:italic><jats:sup>2<\/jats:sup>[0, 1] with finite dimension so that basis elements of these subspaces were orthonormal.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Findings<\/jats:title><jats:p>In this process, solution of Fredholm\u2010Hammerstein integral equation is found by solving the generated system of nonlinear equations.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Originality\/value<\/jats:title><jats:p>Comparing the method with others shows that this system has less computation. In fact, decreasing of computations result from the modification.<\/jats:p><\/jats:sec>","DOI":"10.1108\/03684920910944830","type":"journal-article","created":{"date-parts":[[2009,5,30]],"date-time":"2009-05-30T07:00:39Z","timestamp":1243666839000},"page":"615-620","source":"Crossref","is-referenced-by-count":7,"title":["A modification for solving Fredholm\u2010Hammerstein integral equation by using wavelet basis"],"prefix":"10.1108","volume":"38","author":[{"given":"Mohsen","family":"Rabbani","sequence":"first","affiliation":[]},{"given":"Khosrow","family":"Maleknejad","sequence":"additional","affiliation":[]}],"member":"140","reference":[{"key":"key2022012220130610400_b1","doi-asserted-by":"crossref","unstructured":"Alpert, B.K. 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(2003), \u201cWavelets application to the Petrov\u2010Galerkin method for Hammerstein equations\u201d, Applied Numerical Mathematics, Vol. 45, pp. 255\u201073.","DOI":"10.1016\/S0168-9274(02)00173-3"},{"key":"key2022012220130610400_b6","doi-asserted-by":"crossref","unstructured":"Kaneko, H., Noren, R.D. and Padilla, P.A. (1997), \u201cSupercovergence of the iterated collocation method for Hammerstein equations\u201d, Journal of Computational and Applied Mathematics, Vol. 80, pp. 335\u201049.","DOI":"10.1016\/S0377-0427(97)00040-X"},{"key":"key2022012220130610400_b5","doi-asserted-by":"crossref","unstructured":"Lakestani, M., Razzaghi, M. and Dehgan, M. (2005), \u201cSolution of nonlinear Fredholm Hammerstein integral equation by using semiorthogonal spline wavelets\u201d, Mathematical Problem in Engineering, Vol. 1, pp. 113\u201021.","DOI":"10.1155\/MPE.2005.113"},{"key":"key2022012220130610400_b3","doi-asserted-by":"crossref","unstructured":"Maleknejad, K., Karami, M. and Rabbani, M. (2006), \u201cUsing the Petrov\u2010Galerkin elements for solving Hammerstein integral equations\u201d, Applied Mathematics and Computation, Vol. 172, pp. 831\u201045.","DOI":"10.1016\/j.amc.2005.02.041"}],"container-title":["Kybernetes"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.emeraldinsight.com\/doi\/full-xml\/10.1108\/03684920910944830","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.emerald.com\/insight\/content\/doi\/10.1108\/03684920910944830\/full\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.emerald.com\/insight\/content\/doi\/10.1108\/03684920910944830\/full\/html","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,24]],"date-time":"2025-07-24T23:53:36Z","timestamp":1753401216000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.emerald.com\/k\/article\/38\/3-4\/615-620\/451373"}},"subtitle":[],"editor":[{"given":"Mian\u2010yun","family":"Chen","sequence":"first","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2009,4,10]]},"references-count":7,"journal-issue":{"issue":"3\/4","published-print":{"date-parts":[[2009,4,10]]}},"alternative-id":["10.1108\/03684920910944830"],"URL":"https:\/\/doi.org\/10.1108\/03684920910944830","relation":{},"ISSN":["0368-492X"],"issn-type":[{"type":"print","value":"0368-492X"}],"subject":[],"published":{"date-parts":[[2009,4,10]]}}}