Open AccessOn Saulyev's Methods
Author(s) -
Ole Østerby
Publication year - 2017
Publication title -
daimi pb
Language(s) - English
Resource type - Journals
eISSN - 2245-9316
pISSN - 0105-8517
DOI - 10.7146/dpb.v43i599.26410
Subject(s) - mathematics , derivative (finance) , consistency (knowledge bases) , space (punctuation) , boundary value problem , order (exchange) , stability (learning theory) , second derivative , differential equation , mathematical analysis , pure mathematics , calculus (dental) , computer science , discrete mathematics , medicine , dentistry , finance , machine learning , financial economics , economics , operating system
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.