论文标题
非本地相互作用立方非线性和白噪声分散的Schrödinger方程的分裂方案的收敛速率很强
Strong rates of convergence of a splitting scheme for Schrödinger equations with nonlocal interaction cubic nonlinearity and white noise dispersion
论文作者
论文摘要
我们分析了一个分裂积分器，以通过非局部相互作用立方非线性和白噪声分散体的schrödinger方程时间离散。我们证明，对于某些Sobolev空间中的任何$ p \ geq1 $，这次集成商在$ p $ - th的平均意义中具有收敛顺序。我们证明，分裂方案保留了$ l^2 $ norm，这是证明强大收敛结果的关键属性。最后，数值实验说明了提出的数值方案的性能。
We analyse a splitting integrator for the time discretization of the Schrödinger equation with nonlocal interaction cubic nonlinearity and white noise dispersion. We prove that this time integrator has order of convergence one in the $p$-th mean sense, for any $p\geq1$ in some Sobolev spaces. We prove that the splitting schemes preserves the $L^2$-norm, which is a crucial property for the proof of the strong convergence result. Finally, numerical experiments illustrate the performance of the proposed numerical scheme.
