63 citations · 585 across the 80 of their papers we have counts for
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Energy-preserving exponential integrable numerical method for stochastic cubic wave equation with additive noise
Jianbo Cui, Jialin Hong, Lihai Ji +1
In this paper, we present an energy-preserving exponentially integrable numerical method for stochastic wave equation with cubic nonlinearity and additive noise. We first apply the…
Energy-preserving multi-symplectic Runge-Kutta methods for Hamiltonian wave equations
Chuchu Chen, Jialin Hong, Chol Sim +1
It is well-known that a numerical method which is at the same time geometric structure-preserving and physical property-preserving cannot exist in general for Hamiltonian partial d…
Stochastic modified equations for symplectic methods applied to rough Hamiltonian systems based on the Wong--Zakai approximation
Chuchu Chen, Jialin Hong, Chuying Huang
We investigate the stochastic modified equation which plays an important role in the stochastic backward error analysis for explaining the mathematical mechanism of a numerical met…
Absolute continuity and numerical approximation of stochastic Cahn--Hilliard equation with unbounded noise diffusion
Jianbo Cui, Jialin Hong
In this article, we develop and analyze a full discretization, based on the spatial spectral Galerkin method and the temporal drift implicit Euler scheme, for the stochastic Cahn--…
Wellposedness and regularity estimate for stochastic Cahn--Hilliard equation with unbounded noise diffusion
Jianbo Cui, Jialin Hong
In this article, we consider the stochastic Cahn--Hilliard equation driven by multiplicative space-time white noise with diffusion coefficient of sublinear growth. By introducing t…
Approximation of Invariant Measures for Stochastic Differential Equations with Piecewise Continuous Arguments via Backward Euler Method
Chuchu Chen, Jialin Hong, Yulan Lu
For the stochastic differential equation (SDE) which has piecewise continuous arguments (PCAs), is driven by multiplicative noises and its drift coefficients are dissipative, we sh…
Convergence in Density of Splitting AVF Scheme for Stochastic Langevin Equation
Jianbo Cui, Jialin Hong, Derui Sheng
In this article, we study the density function of the numerical solution of the splitting averaged vector field (AVF) scheme for the stochastic Langevin equation. To deal with the…
The probabilistic superiority of stochastic symplectic methods via large deviations principles
Chuchu Chen, Jialin Hong, Diancong Jin +1
It is well known that symplectic methods have been rigorously shown to be superior to non-symplectic ones especially in long-time computation, when applied to deterministic Hamilto…
Dynamic evaluation of exponential polynomial curves and surfaces via basis transformation
Xunnian Yang, Jialin Hong
It is shown in "SIAM J. Sci. Comput. 39 (2017):B424-B441" that free-form curves used in computer aided geometric design can usually be represented as the solutions of linear differ…
Exponential Integrators for Stochastic Maxwell's Equations Driven by Itô Noise
David Cohen, Jianbo Cui, Jialin Hong +1
This article presents explicit exponential integrators for stochastic Maxwell's equations driven by both multiplicative and additive noises. By utilizing the regularity estimate of…