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In contrast with related methodologies, the novelty of this algorithm is that it is unconditionally stable. And also, the error estimates are proved. Numerical tests illustrate the theoretical properties for the VMEMC method.<\/p><\/jats:p>","DOI":"10.3934\/nhm.2024045","type":"journal-article","created":{"date-parts":[[2024,9,29]],"date-time":"2024-09-29T12:26:06Z","timestamp":1727612766000},"page":"1013-1037","source":"Crossref","is-referenced-by-count":1,"title":["A variational MAX ensemble numerical algorism for a transient heat model with random inputs"],"prefix":"10.3934","volume":"19","author":[{"given":"Tingfu","family":"Yao","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Guizhou University, Guiyang 550025, China"},{"name":"College of Science, Guiyang University, Guiyang 550005, China"}]},{"given":"Changlun","family":"Ye","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Guizhou Normal University, Guiyang 550001, China"}]},{"given":"Xianbing","family":"Luo","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Guizhou University, Guiyang 550025, China"}]},{"given":"Shuwen","family":"Xiang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Guizhou University, Guiyang 550025, China"},{"name":"College of Science, Guiyang University, Guiyang 550005, China"}]}],"member":"2321","reference":[{"key":"key-10.3934\/nhm.2024045-1","doi-asserted-by":"publisher","unstructured":"I. 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