{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T10:42:23Z","timestamp":1740134543999,"version":"3.37.3"},"reference-count":17,"publisher":"Wiley","license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"name":"Funda\u00e7\u00e3o para a Ci\u00eancia e Tecnologia","award":["PEst-OE\/EGE\/UI0491\/2011","304617"],"award-info":[{"award-number":["PEst-OE\/EGE\/UI0491\/2011","304617"]}]},{"DOI":"10.13039\/501100000780","name":"European Commission","doi-asserted-by":"publisher","award":["PEst-OE\/EGE\/UI0491\/2011","304617"],"award-info":[{"award-number":["PEst-OE\/EGE\/UI0491\/2011","304617"]}],"id":[{"id":"10.13039\/501100000780","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Abstract and Applied Analysis"],"published-print":{"date-parts":[[2014]]},"abstract":"<jats:p>We study the spatial discretisation of the Cauchy problem for a multidimensional linear parabolic PDE of second order, with nondivergent operator and unbounded time- and space-dependent coefficients. The equation free term and the initial data are also allowed to grow. Under a nondegeneracy assumption, we consider the PDE solvability in the framework of the variational approach and approximate in space the PDE problem's generalised solution, with the use of finite-difference methods. The rate of convergence is estimated.<\/jats:p>","DOI":"10.1155\/2014\/801059","type":"journal-article","created":{"date-parts":[[2014,3,9]],"date-time":"2014-03-09T05:25:49Z","timestamp":1394342749000},"page":"1-11","source":"Crossref","is-referenced-by-count":0,"title":["Spatial Approximation of Nondivergent Type Parabolic PDEs with Unbounded Coefficients Related to Finance"],"prefix":"10.1155","volume":"2014","author":[{"given":"Fernando F.","family":"Gon\u00e7alves","sequence":"first","affiliation":[{"name":"CEMAPRE & Departmento de Matem\u00e1tica, ISEG, Universidade de Lisboa, Rua do Quelhas 6, 1200-781 Lisboa, Portugal"},{"name":"Universidade Europeia, Estrada da Correia 53, 1500-210 Lisboa, Portugal"}]},{"given":"Maria Ros\u00e1rio","family":"Grossinho","sequence":"additional","affiliation":[{"name":"CEMAPRE & Departmento de Matem\u00e1tica, ISEG, Universidade de Lisboa, Rua do Quelhas 6, 1200-781 Lisboa, Portugal"}]}],"member":"311","reference":[{"year":"1996","key":"13"},{"doi-asserted-by":"publisher","key":"8","DOI":"10.1186\/1687-1847-2012-14"},{"doi-asserted-by":"publisher","key":"9","DOI":"10.1080\/17442509008833653"},{"key":"19","series-title":"Handbook of Numerical Analysis","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/S1570-8659(05)80033-X","volume-title":"Finite difference methods for linear parabolic equations","volume":"1","year":"1990"},{"doi-asserted-by":"publisher","key":"2","DOI":"10.1287\/mnsc.1040.0275"},{"doi-asserted-by":"publisher","key":"10","DOI":"10.1090\/S0025-5718-09-02229-7"},{"doi-asserted-by":"publisher","key":"11","DOI":"10.4310\/MAA.2009.v16.n2.a3"},{"doi-asserted-by":"publisher","key":"12","DOI":"10.1090\/S0025-5718-2011-02478-6"},{"doi-asserted-by":"publisher","key":"1","DOI":"10.1142\/S0218202595000085"},{"doi-asserted-by":"publisher","key":"15","DOI":"10.1016\/j.camwa.2006.09.014"},{"doi-asserted-by":"publisher","key":"18","DOI":"10.1016\/j.cam.2007.01.035"},{"doi-asserted-by":"publisher","key":"17","DOI":"10.1093\/imanum\/23.2.241"},{"doi-asserted-by":"publisher","key":"3","DOI":"10.1137\/0719063"},{"doi-asserted-by":"publisher","key":"4","DOI":"10.1142\/9789812703316_0008"},{"doi-asserted-by":"publisher","key":"5","DOI":"10.1016\/j.apnum.2007.02.002"},{"volume":"1","year":"1968","key":"14"},{"volume":"19","year":"1998","series-title":"Graduate Studies in Mathematics","key":"6"}],"container-title":["Abstract and Applied Analysis"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/aaa\/2014\/801059.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/aaa\/2014\/801059.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/aaa\/2014\/801059.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,6,22]],"date-time":"2017-06-22T05:17:22Z","timestamp":1498108642000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/aaa\/2014\/801059\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"references-count":17,"alternative-id":["801059","801059"],"URL":"https:\/\/doi.org\/10.1155\/2014\/801059","relation":{},"ISSN":["1085-3375","1687-0409"],"issn-type":[{"type":"print","value":"1085-3375"},{"type":"electronic","value":"1687-0409"}],"subject":[],"published":{"date-parts":[[2014]]}}}