DAIMI Report Series https://tidsskrift.dk/daimipb Aarhus University en-US DAIMI Report Series 0105-8517 <p><a href="http://creativecommons.org/licenses/by-nc-nd/3.0/" rel="license"><img style="border-width: 0px;" src="http://i.creativecommons.org/l/by-nc-nd/3.0/80x15.png" alt="Creative Commons License" /></a></p><p>Articles published in DAIMI PB are licensed under a <a href="http://creativecommons.org/licenses/by-nc-nd/3.0/" rel="license">Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License</a>.</p> On Saulyev's Methods https://tidsskrift.dk/daimipb/article/view/26410 <span style="line-height: 107%; font-family: 'Calibri',sans-serif; font-size: 11pt; mso-fareast-font-family: Calibri; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA; mso-ascii-theme-font: minor-latin; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi;" lang="EN-US">In 1957 V. K. Saulyev proposed two so-called asymmetric methods for solving parabolic equations. We study these methods w.r.t. their stability and consistency, how to include first order derivative terms, how to apply boundary conditions with a derivative, and how to extend the methods to two space dimensions. We also prove that the various modifications proposed by Saulyev, Barakat and Clark, and Larkin also (as was to be expected) require k = o(h) in order to be consistent. As a curiosity we show that the two original Saulyev methods in fact solve two different differential equations.</span> Ole Østerby ##submission.copyrightStatement## 2017-04-01 2017-04-01 599 10.7146/dpb.v43i599.26410