{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:33:37Z","timestamp":1787337217680,"version":"build-2736575974"},"reference-count":21,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2010,1]]},"abstract":"<jats:p>In this paper, two new stochastic algorithms for calculating parametric derivatives of the solution to the Smoluchowski coagulation equation are presented. It is assumed that the coagulation kernel is dependent upon these parameters. The new algorithms (called \u201cSingle\u201d and \u201cDouble\u201d) work by coupling two Marcus\u2013Lushnikov processes in such a way as to reduce the difference between their trajectories, thereby significantly reducing the variance of central difference estimators of the parametric derivatives. In the numerical results, the algorithms are shown to have an $O(1\/N)$ order of convergence as expected, where N is the initial number of particles. It was also found that the Single and Double Algorithms provide much smaller variances. Furthermore, a method for establishing \u201cefficiency\u201d is considered, which takes into account the variances as well as CPU run times, and the \u201cDouble\u201d is significantly more \u201cefficient\u201d compared to the \u201cIndependent\u201d Algorithm in most cases.<\/jats:p>","DOI":"10.1137\/09075679x","type":"journal-article","created":{"date-parts":[[2010,2,17]],"date-time":"2010-02-17T18:07:17Z","timestamp":1266430037000},"page":"635-655","source":"Crossref","is-referenced-by-count":7,"title":["Coupling Algorithms for Calculating Sensitivities of Smoluchowski's Coagulation Equation"],"prefix":"10.1137","volume":"32","author":[{"given":"Peter L. W.","family":"Man","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"James R.","family":"Norris","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Isma\u00ebl F.","family":"Bailleul","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Markus","family":"Kraft","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2010,2,17]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1214\/aoap\/1015345398"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827599353488"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.2002.7192"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1515\/156939603322601950"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1002\/aic.10881"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1016\/j.powtec.2006.12.010"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1016\/j.ces.2007.05.028"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1016\/j.combustflame.2007.04.012"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2008.10.033"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2004.03.006"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1016\/j.ces.2006.03.009"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1002\/aic.10735"},{"key":"R13","doi-asserted-by":"crossref","unstructured":"S. Asmussen and P. W. Glynn,\n                      Stochastic Simulation: Algorithms and Analysis\n                      , Springer, New York, 2007, pp. 224\u2013230.","DOI":"10.1007\/978-0-387-69033-9"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1137\/040618953"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1214\/aoap\/1029962598"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1007\/s002200050368"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1016\/j.combustflame.2006.02.005"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1016\/j.proci.2006.08.021"},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1016\/j.combustflame.2006.10.007"},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.2307\/3318611"},{"key":"R21","doi-asserted-by":"crossref","unstructured":"P. L. W. Man, M. Kraft, and J. R. Norris,\n                      Coupling algorithms for calculating sensitivities of population balances\n                      , in Numerical Analysis and Applied Mathematics, AIP Conf. Proc. 1048, Amer. Inst. Phys., Melville, NY, 2008, pp. 927\u2013930.","DOI":"10.1063\/1.2991086"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/09075679X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:50:07Z","timestamp":1787334607000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/09075679X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,1]]},"references-count":21,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2010,1]]}},"alternative-id":["10.1137\/09075679X"],"URL":"https:\/\/doi.org\/10.1137\/09075679x","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,1]]}}}