报告题目 (Title)：An efficient time-two mesh compact ADI method for nonlinear Schrodinger equations with error analysis
中文题目：针对非线性薛定谔方程的高效双时间网格紧致交替方向方法及其误差分析
报告人 (Speaker)：何斯日古楞 教授， 呼和浩特民族学院
报告时间 (Time)：2025年4月19日 (周六) 9:00
报告地点 (Place)：校本部GJ303
邀请人(Inviter)：纪丽洁
摘要：A time two-mesh algorithm combined with compact difference ADI scheme is proposed for solving the two-dimensional nonlinear Schrodinger equation. This algorithm contains three steps: first, a nonlinear implicit system is solved on the time coarse mesh by ADI technique; next, based on the coarse mesh solutions, some useful values on the time fine mesh are provided by applying the Lagrange's linear interpolation formula; finally, a linear system is solved on the time fine mesh. Taking advantage of the discrete energy and the mathematical induction methods, result with 
in the discrete L2 norm and H1 norm are deduced, respectively. Numerical experiments on some model problems show that the porposed algorithm preserve the conservation laws of charge and energy and is very effective. Here, 
and 
are the temporal parameters on the coarse and fine mesh, respectively, and 
is the space step.