DuFort--Frankel-Type Methods for Linear and Nonlinear Schrödinger Equations

In this paper we propose a so-called DuFort--Frankel-type method for the linear and nonlinear Schrodinger equations. Schemes of the DuFort--Frankel type are explicit and have solution-independent stability criteria. Moreover, the DuFort--Frankel-type method satisfies a discrete conservation law for the Schrodinger equations, and this is important to get reliable numerical solutions.