关于解Schrdinger方程组的隐式差分格式

On Implicit Difference Schemes for Solving the Schrodinger Systems

非线性Schrdjnger方程组是物理学中重要的方程组,它在许多地方有着重要的应用,所以近来有许多文章讨论它的解的存在性和数值解法。在数值解法中,差分方法的研究占有重要的比重。随着隐式差分格式的优点越来越被人们认识,因此不少作者提出了各种隐式格式及其理论分析技巧。

The implicit difference schemes are important methods for solving numerically the nonlinear Schrodinger systems and, therefore, the theoretical problems concerning these schemes are called for efficient treatment. In this paper, we use a method proposed by the author to analyse, as an example, the nonlinearly implicit scheme in[2]and prove the existence,uniqueness, stability and convergence of the solution to the scheme. The analysis method can also be applied to many other nonlinearly implicit schemes.