{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T12:38:36Z","timestamp":1773405516259,"version":"3.50.1"},"reference-count":16,"publisher":"Emerald","issue":"9","license":[{"start":{"date-parts":[[2009,10,16]],"date-time":"2009-10-16T00:00:00Z","timestamp":1255651200000},"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":[[2009,10,16]]},"abstract":"<jats:sec><jats:title content-type=\"abstract-heading\">Purpose<\/jats:title><jats:p>The purpose of this paper is to provide a Monte Carlo variance reduction method based on Control variates to solve Fredholm integral equations of the second kind.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Design\/methodology\/approach<\/jats:title><jats:p>A numerical algorithm consisted of the combined use of the successive substitution method and Monte Carlo simulation is established for the solution of Fredholm integral equations of the second kind.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Findings<\/jats:title><jats:p>Owing to the application of the present method, the variance of the solution is reduced. Therefore, this method achieves several orders of magnitude improvement in accuracy over the conventional Monte Carlo method.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Practical implications<\/jats:title><jats:p>Numerical tests are performed in order to show the efficiency and accuracy of the present paper. Numerical experiments show that an excellent estimation on the solution can be obtained within a couple of minutes CPU time at Pentium IV\u20102.4\u2009GHz PC.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Originality\/value<\/jats:title><jats:p>This paper provides a new efficient method to solve Fredholm integral equations of the second kind and discusses basic advantages of the present method.<\/jats:p><\/jats:sec>","DOI":"10.1108\/03684920910991577","type":"journal-article","created":{"date-parts":[[2009,10,17]],"date-time":"2009-10-17T07:04:19Z","timestamp":1255763059000},"page":"1621-1629","source":"Crossref","is-referenced-by-count":4,"title":["Monte Carlo simulation for solving Fredholm integral equations"],"prefix":"10.1108","volume":"38","author":[{"given":"Rahman","family":"Farnoosh","sequence":"first","affiliation":[]},{"given":"Ebrahimi","family":"Morteza","sequence":"additional","affiliation":[]}],"member":"140","reference":[{"key":"key2022021320255181100_b1","unstructured":"Albert, G.E. (1956), \u201cA general theory of stochastic estimates of the Neumann series for solution of certain Fredholm integral equations and related series\u201d, Symposium of Monte Carlo Methods, Wiley, New York, NY."},{"key":"key2022021320255181100_b2","unstructured":"Cao, Y., Hussaini, M.Y., Zang, T. and Zatezalo, A. (2003), \u201cAn efficient Monte Carlo method for optimal control problems with uncertainty\u201d, Applied Numerical Mathematics, Vol. 26, pp. 219\u201030."},{"key":"key2022021320255181100_b3","doi-asserted-by":"crossref","unstructured":"Ermolyev, Y.M. (1969), \u201cOn the method of generalized stochastic gradients and quasi\u2010Fejer\u2010sequences\u201d, Cybernetics, Vol. 5, pp. 208\u201020.","DOI":"10.1007\/BF01071091"},{"key":"key2022021320255181100_b4","doi-asserted-by":"crossref","unstructured":"Farnoosh, R. and Ebrahimi, M. 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