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Unconditional L∞ convergence of a compact ADI scheme for coupled nonlinear Schrödinger system
Applied Numerical Mathematics ( IF 2.8 ) Pub Date : 2020-07-01 , DOI: 10.1016/j.apnum.2020.03.006
Juan Chen , Fangqi Chen

Abstract In this paper, a three-level compact alternating direction implicit (ADI) scheme is formulated for the two-dimensional coupled nonlinear Schrodinger 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.

中文翻译:

耦合非线性薛定谔系统的紧凑ADI方案的无条件L∞收敛

摘要 本文针对二维耦合非线性薛定谔系统制定了一种三级紧凑交替方向隐式(ADI)方案。通过使用一个重要的新引理和数学归纳法,证明了紧凑型 ADI 方案在 L ∞ 范数上无条件收敛,时间收敛阶数为 2,空间收敛阶数为 4。已经进行了数值实验以支持理论结果并显示新方法的效率。
更新日期:2020-07-01
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