无阶数降低的非线性薛定谔方程的分裂方法
Splitting methods for nonlinear Schrödinger equation without order reduction
AI总结：
研究具有时间相关狄利克雷边界条件的非线性薛定谔方程，基于Strang方法用高阶吉田分裂积分，通过修改Strang方法，无需数据微分，该方法适用于相关问题并能获得局部三阶和全局二阶。
摘要：
本文提供了一种技术，用于将具有时间相关狄利克雷边界条件的非线性薛定谔方程与基于Strang方法的高阶吉田分裂进行积分。为此，需要对Strang方法进行修改，其中方程的线性和刚性部分用类似有理的中点规则进行积分，所需边界值无需数据微分即可计算。尽管吉田分裂（实系数）因稳定性不能应用于抛物问题以获得高于二阶的阶数，但修改后的Strang方法也适用于此类问题，且无需数据微分即可获得局部三阶和全局二阶。
英文摘要：
A technique is provided in this paper to integrate nonlinear Schrödinger equation with time-dependent Dirichlet boundary conditions with high-order Yoshida splittings which are based on Strang method. For that, a modification of Strang method is required in which the linear and stiff part of the equation is integrated with a rational-like version of midpoint rule for which the required boundary values can be calculated without resorting to any differentiation of data. Although Yoshida splitting (with real coefficients) cannot be applied to parabolic problems to obtain order higher than two because of stability, the modified Strang method is also applicable to such type of problems and local order $3$ and global order $2$ are also obtained without differentiation of data.
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