68 citations · 316 across the 16 of their papers we have counts for
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Optimal Error Estimates of Conservative Local Discontinuous Galerkin Method for Nonlinear Schrödinger Equation
Jialin Hong, Lihai Ji, Zhihui Liu
In this paper, we propose a conservative local discontinuous Galerkin method for one-dimensional nonlinear Schrödinger equation. By using special upwind-biased numerical fluxes, we…
Strong Convergence Rate of Finite Difference Approximations for Stochastic Cubic Schrödinger Equations
Jianbo Cui, Jialin Hong, Zhihui Liu
In this paper, we derive a strong convergence rate of spatial finite difference approximations for both focusing and defocusing stochastic cubic Schrödinger equations driven by a m…
Optimal Hölder Continuity and Hitting Probabilities for SPDEs with Rough Fractional Noises
Jialin Hong, Zhihui Liu, Derui Sheng
We investigate the optimal Hölder continuity and hitting probabilities for systems of stochastic heat equations and stochastic wave equations driven by an additive fractional Brown…
Stochastic Symplectic and Multi-Symplectic Methods for Nonlinear Schrödinger Equation with White Noise Dispersion
Jianbo Cui, Jialin Hong, Zhihui Liu +1
We indicate that the nonlinear Schrödinger equation with white noise dispersion possesses stochastic symplectic and multi-symplectic structures. Based on these structures, we propo…
Approximating Stochastic Evolution Equations with Additive White and Rough Noises
Yanzhao Cao, Jialin Hong, Zhihui Liu
In this paper, we analyze Galerkin approximations for stochastic evolution equations driven by an additive Gaussian noise which is temporally white and spatially fractional with Hu…