63 citations · 585 across the 80 of their papers we have counts for
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Novel physical property preserved methods for stochastic Schrödinger--KdV equation
Ziheng Chen, Jialin Hong, Liying Sun
In this work, we study the stochastic Schrödinger--KdV equation driven by additive noise from both analytical and numerical viewpoints. We first establish the evolution laws for th…
Error analysis of numerical methods on graded meshes for stochastic Volterra equations
Xinjie Dai, Jialin Hong, Derui Sheng
This paper presents the error analysis of numerical methods on graded meshes for stochastic Volterra equations with weakly singular kernels. We first prove a novel regularity estim…
Novel structure-preserving schemes for stochastic Klein--Gordon--Schrödinger equations with additive noise
Jialin Hong, Baohui Hou, Liying Sun +1
Stochastic Klein--Gordon--Schrödinger (KGS) equations are important mathematical models and describe the interaction between scalar nucleons and neutral scalar mesons in the stocha…
Novel structure-preserving schemes for stochastic Klein--Gordon--Schrödinger equations with additive noise
Jialin Hong, Baohui Hou, Liying Sun +1
Stochastic Klein--Gordon--Schrödinger (KGS) equations are important mathematical models and describe the interaction between scalar nucleons and neutral scalar mesons in the stocha…
Superiority Of Symplectic Methods For Stochastic Hamiltonian System Via Asymptotic Error Distribution
Jialin Hong, Ge Liang, Derui Sheng
The superiority of symplectic methods for stochastic Hamiltonian systems has been widely recognized, yet the probabilistic mechanism behind this superiority remains incompletely un…
An adaptive time-stepping fully discrete scheme for stochastic NLS equation: Strong convergence and numerical asymptotics
Chuchu Chen, Tonghe Dang, Jialin Hong
In this paper, we propose and analyze an adaptive time-stepping fully discrete scheme which possesses the optimal strong convergence order for the stochastic nonlinear Schrödinger…
Ergodic numerical approximations for stochastic Maxwell equations
Chuchu Chen, Jialin Hong, Lihai Ji +1
In this paper, we propose a novel kind of numerical approximations to inherit the ergodicity of stochastic Maxwell equations. The key to proving the ergodicity lies in the uniform…
Scheme-Induced Minimum Action Methods for SPDEs: A Variational Framework for Convergence Analysis
Jialin Hong, Diancong Jin, Derui Sheng
The minimum action method (MAM) is an important numerical tool for computing the most probable transition paths and the leading exponential rates of rare-event probabilities for st…
Semi-implicit energy-preserving numerical schemes for stochastic wave equation via SAV approach
Jianbo Cui, Jialin Hong, Liying Sun
In this paper, we propose and analyze semi-implicit numerical schemes for the stochastic wave equation (SWE) with general nonlinearity and multiplicative noise. These numerical sch…
Mittag--Leffler Euler integrator and large deviations for stochastic space-time fractional diffusion equations
Xinjie Dai, Jialin Hong, Derui Sheng
Stochastic space-time fractional diffusion equations often appear in the modeling of the heat propagation in non-homogeneous medium. In this paper, we firstly investigate the Mitta…
Density convergence of a fully discrete finite difference method for stochastic Cahn--Hilliard equation
Jialin Hong, Diancong Jin, Derui Sheng
This paper focuses on investigating the density convergence of a fully discrete finite difference method when applied to numerically solve the stochastic Cahn--Hilliard equation dr…
Convergence analysis of a finite difference method for stochastic Cahn--Hilliard equation
Jialin Hong, Diancong Jin, Derui Sheng
This paper presents the convergence analysis of the spatial finite difference method (FDM) for the stochastic Cahn--Hilliard equation with Lipschitz nonlinearity and multiplicative…
Three kinds of novel multi-symplectic methods for stochastic Hamiltonian partial differential equations
Jialin Hong, Baohui Hou, Qiang Li +1
Stochastic Hamiltonian partial differential equations, which possess the multi-symplectic conservation law, are an important and fairly large class of systems. The multi-symplectic…
Strong error analysis of Euler methods for overdamped generalized Langevin equations with fractional noise: Nonlinear case
Xinjie Dai, Jialin Hong, Derui Sheng +1
This paper considers the strong error analysis of the Euler and fast Euler methods for nonlinear overdamped generalized Langevin equations driven by the fractional noise. The main…
Structure-preserving splitting methods for stochastic logarithmic Schrödinger equation via regularized energy approximation
Jianbo Cui, Jialin Hong, Liying Sun
In this paper, we study two kinds of structure-preserving splitting methods, including the Lie--Trotter type splitting method and the finite difference type method, for the stochas…
Strong convergence of adaptive time-stepping schemes for the stochastic Allen--Cahn equation
Chuchu Chen, Tonghe Dang, Jialin Hong
It is known in \cite{beccari} that the standard explicit Euler-type scheme (such as the exponential Euler and the linear-implicit Euler schemes) with a uniform timestep, though com…
Large deviations principles of sample paths and invariant measures of numerical methods for parabolic SPDEs
Chuchu Chen, Ziheng Chen, Jialin Hong +1
For parabolic stochastic partial differential equations (SPDEs), we show that the numerical methods, including the spatial spectral Galerkin method and further the full discretizat…
Energy-preserving fully-discrete schemes for nonlinear stochastic wave equations with multiplicative noise
Jialin Hong, Baohui Hou, Liying Sun
In this paper, we focus on constructing numerical schemes preserving the averaged energy evolution law for nonlinear stochastic wave equations driven by multiplicative noise. We fi…
Influences of Numerical Discretizations on Hitting Probabilities for Linear Stochastic Parabolic System
Chuchu Chen, Jialin Hong, Derui Sheng
This paper investigates the influences of standard numerical discretizations on hitting probabilities for linear stochastic parabolic system driven by space-time white noises. We e…
Weak intermittency and second moment bound of a fully discrete scheme for stochastic heat equation
Chuchu Chen, Tonghe Dang, Jialin Hong
In this paper, we first prove the weak intermittency, and in particular the sharp exponential order of the second moment of the exact solution of the stochastic heat equati…
A new efficient operator splitting method for stochastic Maxwell equations
Chuchu Chen, Jialin Hong, Lihai Ji
This paper proposes and analyzes a new operator splitting method for stochastic Maxwell equations driven by additive noise, which not only decomposes the original multi-dimensional…
A splitting semi-implicit method for stochastic incompressible Euler equations on
Jialin Hong, Derui Sheng, Tau Zhou
The main difficulty in studying numerical method for stochastic evolution equations (SEEs) lies in the treatment of the time discretization (J. Printems. [ESAIM Math. Model. Numer.…
Numerically asymptotical preservation of the large deviations principles for invariant measures of Langevin equations
Jialin Hong, Diancong Jin, Derui Sheng +1
In this paper, we focus on two kinds of large deviations principles (LDPs) of the invariant measures of Langevin equations and their numerical methods, as the noise intensity $ε\to…
Super-convergence analysis on exponential integrator for stochastic heat equation driven by additive fractional Brownian motion
Jialin Hong, Chuying Huang
In this paper, we consider the strong convergence order of the exponential integrator for the stochastic heat equation driven by an additive fractional Brownian motion with Hurst p…