{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:13:49Z","timestamp":1753881229732,"version":"3.41.2"},"reference-count":21,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2012,9,4]],"date-time":"2012-09-04T00:00:00Z","timestamp":1346716800000},"content-version":"vor","delay-in-days":247,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"name":"Vietnam National Foundation for Science and Technology Development","award":["102.99\u20132011.24"],"award-info":[{"award-number":["102.99\u20132011.24"]}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2012,1]]},"abstract":"<jats:p>Solving boundary value problems (BVPs) for the fourth\u2010order differential equations by the reduction of them to BVPs for the second\u2010order equations with the aim to use the achievements for the latter ones attracts attention from many researchers. In this paper, using the technique developed by ourselves in recent works, we construct iterative method for the second BVP for biharmonic\u2010type equation, which describes the deflection of a plate resting on a biparametric elastic foundation. The convergence rate of the method is established. The optimal value of the iterative parameter is found. Several numerical examples confirm the efficiency of the proposed method.<\/jats:p>","DOI":"10.1155\/2012\/891519","type":"journal-article","created":{"date-parts":[[2012,9,4]],"date-time":"2012-09-04T21:01:53Z","timestamp":1346792513000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Iterative Method for Solving the Second Boundary Value Problem for Biharmonic\u2010Type Equation"],"prefix":"10.1155","volume":"2012","author":[{"given":"Dang","family":"Quang A.","sequence":"first","affiliation":[]},{"given":"Nguyen","family":"Van Thien","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2012,9,4]]},"reference":[{"key":"e_1_2_7_1_2","first-page":"393","article-title":"On some approches to the solution of the stationary Navier-Stock equation","volume":"8","author":"Dorodnisyn A.","year":"1968","journal-title":"Journal of Computational Mathematics and Mathematical Physics"},{"volume-title":"Analyse Numerique Des Inequations Variationelles","year":"1976","author":"Glowinski R.","key":"e_1_2_7_2_2"},{"key":"e_1_2_7_3_2","first-page":"43","article-title":"On the expansion of the Dirichlet problem and a mixed problem for biharmonic equation into a seriaes of decomposed problems","volume":"6","author":"Palsev B. 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