数学
趋同(经济学)
非线性系统
数值分析
应用数学
辛几何
班级(哲学)
跟踪(心理语言学)
力矩(物理)
指数函数
数学分析
经典力学
量子力学
哲学
经济
人工智能
计算机科学
物理
经济增长
语言学
作者
Charles-Édouard Bréhier,David Cohen
标识
DOI:10.1016/j.apnum.2023.01.002
摘要
We analyze the qualitative properties and the order of convergence of a splitting scheme for a class of nonlinear stochastic Schrödinger equations driven by additive noise. The class of nonlinearities of interest includes nonlocal interaction cubic nonlinearities. We show that the numerical solution is symplectic and preserves the expected mass for all times (trace formula). On top of that, for the convergence analysis, some exponential moment bounds for the exact and numerical solutions are proved. This enables us to provide strong orders of convergence as well as orders of convergence in probability and almost surely. Finally, extensive numerical experiments illustrate the performance of the proposed numerical scheme.
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