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At each time level, the scheme determines the intermediate solution along horizontal lines and the approximate solution along vertical lines passing through the Gauss points. Only at the last time level is the approximate solution along vertical lines converted into the approximate solution defined on the entire rectangular polygon. This property of our approach leads to its efficient implementation and its applicability to rectangular polygons.<\/jats:p>","DOI":"10.1137\/050627885","type":"journal-article","created":{"date-parts":[[2006,8,24]],"date-time":"2006-08-24T15:30:00Z","timestamp":1156433400000},"page":"1054-1077","source":"Crossref","is-referenced-by-count":14,"title":["An Alternating-Direction Implicit Orthogonal Spline Collocation Scheme for Nonlinear Parabolic Problems on Rectangular Polygons"],"prefix":"10.1137","volume":"28","author":[{"given":"Bernard","family":"Bialecki","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ryan I.","family":"Fernandes","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,8,4]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","unstructured":"V. K. Bangia, C. Bennett, A. Reynolds, R. Raghavan, and G. 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