Implicit Difference Schemes for the Generalized Non-Linear Schrödinger System

Abstract

In this paper we prove under certain weak conditions that two classes of implicit difference schemes for the generalized non-linear schrödinger system are convergent and that an iteration method for the corresponding non-linear difference equation is convergent. Therefore, quite a complete theoretical foundation of implicit schemes for the generalized non-linear Schrödinger system is established in this paper.