In this paper, a linearized Euler Galerkin scheme is studied and the unconditionally optimal error estimate in L2-norm is obtained for Schrödinger equation with cubic nonlinearity without any time-step restriction. The key to the analysis is to bound the H1-norm between the numerical solution and the Ritz projection of the exact solution by mathematical induction for two cases rather than the error splitting technique used in the previous work. Finally, some numerical results are presented to confirm the theoretical analysis.

中文翻译：

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具有三次非线性的薛定谔方程的线性化 Euler Galerkin 方案的新误差分析


本文研究了线性欧拉伽辽金方案，并获得了具有三次非线性且没有任何时间步长限制的薛定谔方程在 L2 范数中的无条件最优误差估计。分析的关键是通过数学归纳对两种情况，而不是之前工作中使用的误差拆分技术，将数值解和精确解的 Ritz 投影之间的 H1 范数绑定在一起。最后，给出了一些数值结果，以验证理论分析。