Abstract
In this paper, a three-level compact alternating direction implicit (ADI) scheme is formulated for the two-dimensional coupled nonlinear Schrödinger system. By using an important new lemma and a mathematical induction method, it is proved that the compact ADI scheme is unconditionally convergent in L∞ norm with the convergence order of two in time and four in space. Numerical experiments have been conducted to support the theoretical results and show the efficiency of the new method.
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