论文标题
分析一类非线性随机schrödinger方程的分裂方案
Analysis of a splitting scheme for a class of nonlinear stochastic Schrödinger equations
论文作者
论文摘要
我们分析了由添加剂噪声驱动的一类非线性随机schrödinger方程的定性特性和分裂方案的收敛顺序。感兴趣的非线性类别包括非局部相互作用的立方非线性。我们表明，数值解决方案是符合性的，并保留了所有时间的预期质量。最重要的是，对于收敛分析，证明了确切和数值解的一些指数力矩边界。这使我们能够提供强大的融合顺序以及几乎肯定的概率融合顺序。最后，广泛的数值实验说明了提出的数值方案的性能。
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 Itô 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. 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.
