On Saulyev's Methods

Resumé

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.