汇报标题 (Title)：An efficient time-two mesh compact ADI method for nonlinear Schrodinger equations with error analysis（针对非线性薛定谔方程的高效双功夫网格紧致交替方向步骤及其误差分析）
汇报人 (Speaker)：何斯日古楞 教授 （呼和浩特民族学院）
汇报功夫 (Time)：2025年4月19日 (周六) 9:00
汇报地址 (Place)：校本部GJ303
约请人(Inviter)：纪丽洁
主办部门：理学院数学系
提要：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.
