{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T12:07:09Z","timestamp":1740139629333,"version":"3.37.3"},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"3","funder":[{"DOI":"10.13039\/501100006769","name":"Russian Science Foundation","doi-asserted-by":"crossref","award":["14-11-00083"],"award-info":[{"award-number":["14-11-00083"]}],"id":[{"id":"10.13039\/501100006769","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2014,9,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>We present in this paper a further development of the stochastic spectral method for solving boundary value problems\nin domains which are composed by a set of overlapped discs first suggested by the first author in Appl. Math. Comput. 219 (2013), no. 10, 5123\u20135139].\nWe study statistical characteristics of the solution to isotropic diffusion problem in response to fluctuating\nincoming flux of particles through the circular-shaped boundaries.\nPerformance of the method is illustrated by a series of numerical experiments.\nThe method can be considered as a direct inversion of the integral Poisson formula\nrepresenting the solution in the disc, so it is highly accurate and fast for the class of domains considered.\nThis makes possible to solve an ensemble of equations with random samples of boundary conditions\nand calculate the desired statistical characteristics.<\/jats:p>","DOI":"10.1515\/mcma-2014-0001","type":"journal-article","created":{"date-parts":[[2014,8,19]],"date-time":"2014-08-19T17:00:27Z","timestamp":1408467627000},"page":"173-180","source":"Crossref","is-referenced-by-count":0,"title":["A spectral method for isotropic diffusion equation with random concentration fluctuations of incoming flux of particles through circular-shaped boundaries"],"prefix":"10.1515","volume":"20","author":[{"given":"Karl K.","family":"Sabelfeld","sequence":"first","affiliation":[{"name":"Institute of Computational Mathematics and Mathematical Geophysics, Russian Academy of Sciences, NSU, Novosibirsk, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alexander I.","family":"Levykin","sequence":"additional","affiliation":[{"name":"Institute of Computational Mathematics and Mathematical Geophysics, Russian Academy of Sciences, NSU, Novosibirsk, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2014,8,19]]},"container-title":["Monte Carlo Methods and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mcma-2014-0001\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mcma-2014-0001\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,1]],"date-time":"2023-04-01T19:17:46Z","timestamp":1680376666000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mcma-2014-0001\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,8,19]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2014,5,10]]},"published-print":{"date-parts":[[2014,9,1]]}},"alternative-id":["10.1515\/mcma-2014-0001"],"URL":"https:\/\/doi.org\/10.1515\/mcma-2014-0001","relation":{},"ISSN":["0929-9629","1569-3961"],"issn-type":[{"type":"print","value":"0929-9629"},{"type":"electronic","value":"1569-3961"}],"subject":[],"published":{"date-parts":[[2014,8,19]]}}}