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This new technique retains and improves the convergence properties to the stationary solution. When compared with the conventional dual time-stepping, the method with two derivatives reduces the stiffness of the problem and requires fewer iterations for full convergence to steady-state. In the current formulation, these positive effects require that an approximation of the square root of the spatial operator is available and inexpensive.<\/jats:p>","DOI":"10.1007\/s10915-019-01047-5","type":"journal-article","created":{"date-parts":[[2019,9,9]],"date-time":"2019-09-09T09:02:46Z","timestamp":1568019766000},"page":"1050-1071","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Dual Time-Stepping Using Second Derivatives"],"prefix":"10.1007","volume":"81","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7972-6183","authenticated-orcid":false,"given":"Jan","family":"Nordstr\u00f6m","sequence":"first","affiliation":[]},{"given":"Andrea A.","family":"Ruggiu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,9,9]]},"reference":[{"key":"1047_CR1","doi-asserted-by":"crossref","unstructured":"Jameson, A.: Time dependent calculations using multigrid, with applications to unsteady flows past airfoils and wings. 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