68 citations · 316 across the 16 of their papers we have counts for
11 papers · 1 filter
Numerical Ergodicity and Uniform Estimate of Monotone SPDEs Driven by Multiplicative Noise
Zhihui Liu
We analyze the long-time behavior of numerical schemes for a class of monotone stochastic partial differential equations (SPDEs) driven by multiplicative noise. By deriving several…
-Convergence Rate of Backward Euler Schemes for Monotone SDEs
Zhihui Liu
We give a unified method to derive the strong convergence rate of the backward Euler scheme for monotone SDEs in -norm, with general . The results are applied to t…
Strong Approximation of Monotone Stochastic Partial Differential Equations Driven by Multiplicative Noise
Zhihui Liu, Zhonghua Qiao
We establish a general theory of optimal strong error estimation for numerical approximations of a second-order parabolic stochastic partial differential equation with monotone dri…
Strong convergence of numerical discretizations for semilinear stochastic evolution equations driven by multiplicative white noise
Jialin Hong, Chuying Huang, Zhihui Liu
For semilinear stochastic evolution equations whose coefficients are more general than the classical global Lipschitz, we present results on the strong convergence rates of numeric…
Strong Approximation of Stochastic Allen-Cahn Equation with White Noise
Zhihui Liu, Zhonghua Qiao
We establish an optimal strong convergence rate of a fully discrete numerical scheme for second order parabolic stochastic partial differential equations with monotone drifts, incl…
Strong Convergence Rate of Splitting Schemes for Stochastic Nonlinear Schrödinger Equations
Jianbo Cui, Jialin Hong, Zhihui Liu +1
We prove the optimal strong convergence rate of a fully discrete scheme, based on a splitting approach, for a stochastic nonlinear Schrödinger (NLS) equation. The main novelty of o…
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…
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…
Well-posedness and Finite Element Approximations for Elliptic SPDEs with Gaussian Noises
Yanzhao Cao, Jialin Hong, Zhihui Liu
The paper studies the well-posedness and optimal error estimates of spectral finite element approximations for the boundary value problems of semi-linear elliptic SPDEs driven by w…
Finite element approximations for second order stochastic differential equation driven by fractional Brownian motion
Yanzhao Cao, Jialin Hong, Zhihui Liu
We consider finite element approximations for a one dimensional second order stochastic differential equation of boundary value type driven by a fractional Brownian motion with Hur…