{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,2]],"date-time":"2025-10-02T05:55:45Z","timestamp":1759384545556,"version":"3.37.3"},"reference-count":24,"publisher":"Wiley","license":[{"start":{"date-parts":[[2018,1,1]],"date-time":"2018-01-01T00:00:00Z","timestamp":1514764800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100006319","name":"Centre National pour la Recherche Scientifique et Technique","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100006319","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Moroccan Ministry of High Education and Scientific Research"},{"name":"Deanship of Scientific Research (DSR) at King Abdulaziz University"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2018]]},"abstract":"<jats:p>Some methodological approaches based on generalized polynomial chaos for linear differential equations with random parameters following various types of distribution laws are proposed. Mainly, an internal random coefficients method \u2018IRCM\u2019 is elaborated for a large number of random parameters. A procedure to build a new polynomial chaos basis and a connection between the one-dimensional and multidimensional polynomials are developed. This allows handling easily random parameters with various laws. A compact matrix formulation is given and the required matrices and scalar products are explicitly presented. For random excitations with an arbitrary number of uncertain variables, the IRCM is couplet to the superposition method leading to successive random differential equations with the same main random operator and right-hand sides depending only on one random parameter. This methodological approach leads to equations with a reduced number of random variables and thus to a large reduction of CPU time and memory required for the numerical solution. The conditional expectation method is also elaborated for reference solutions as well as the Monte-Carlo procedure. The applicability and effectiveness of the developed methods are demonstrated by some numerical examples.<\/jats:p>","DOI":"10.1155\/2018\/7403745","type":"journal-article","created":{"date-parts":[[2018,5,21]],"date-time":"2018-05-21T19:31:35Z","timestamp":1526931095000},"page":"1-23","source":"Crossref","is-referenced-by-count":3,"title":["Numerical Procedures for Random Differential Equations"],"prefix":"10.1155","volume":"2018","author":[{"given":"Mohamed","family":"Ben Said","sequence":"first","affiliation":[{"name":"Mathematical Modeling and Control, Department of Mathematics, Faculty of Sciences and Techniques of Tangier, Abdelmalek Essaadi University, Tangier, Morocco"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0493-9029","authenticated-orcid":true,"given":"Lahcen","family":"Azrar","sequence":"additional","affiliation":[{"name":"Research Center STIS, Department of Applied Mathematics and Informatics, ENSET, Mohammed V University, Rabat, Morocco"},{"name":"Department of Mechanical Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Driss","family":"Sarsri","sequence":"additional","affiliation":[{"name":"LTI, Ecole Nationale des Sciences Appliqu\u00e9es de Tanger, Abdelmalek Essaadi University, Tangier, Morocco"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1016\/0045-7949(72)90043-0"},{"year":"2000","key":"3"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-3094-6"},{"year":"2010","key":"5"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.2307\/2371268"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-4730(97)00013-1"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827501387826"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2008.11.007"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1016\/j.engstruct.2009.07.005"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-6911(98)00108-X"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1016\/0266-8920(93)90019-R"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1016\/S0266-8920(97)00020-9"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-4730(97)00013-1"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1061\/(ASCE)0733-9399(1994)120:12(2660)"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2004.05.031"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2010.03.013"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2014.09.032"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1016\/j.probengmech.2003.11.017"},{"year":"2001","series-title":"Bratislava preprint series","key":"20"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1051\/m2an\/2011045"},{"key":"22","doi-asserted-by":"publisher","DOI":"10.1016\/j.compstruc.2010.11.009"},{"key":"23","doi-asserted-by":"publisher","DOI":"10.1080\/15376494.2015.1029155"},{"key":"24","doi-asserted-by":"publisher","DOI":"10.1016\/j.asej.2015.03.005"},{"key":"25","doi-asserted-by":"publisher","DOI":"10.1007\/BF02863594"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2018\/7403745.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2018\/7403745.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2018\/7403745.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2018,5,21]],"date-time":"2018-05-21T19:31:43Z","timestamp":1526931103000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/jam\/2018\/7403745\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018]]},"references-count":24,"alternative-id":["7403745","7403745"],"URL":"https:\/\/doi.org\/10.1155\/2018\/7403745","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2018]]}}}