I am an assistant professor at Department of Applied Mathematics, PolyU. Before that, I was a visiting assistant professor at School of Mathematics, Georgia Tech worked with Prof. Luca Dieci and Prof. Haomin Zhou. I did my PhD at Academy of Mathematics and Systems Science, CAS, where I was supervised by Prof. Jialin Hong.
Email / Google Scholar / AMS / ORCiD
Strong and weak convergence of numerical methods for stochastic nonlinear Schoedinger equation.
Optimal control on graph and its applications.
Strong Convergence Rate of Numerical Approximations of SPDEs with Non-globally Lipschitz Coefficients
Weak convergence rate and long-time behaviors of numerical approximations for SPDEs
My current research interests include numerical analysis, stochastic ODEs and PDEs, optimal transport, optimal control, structure-preserving algorithms, Hamiltonian systems, dynamical systems, ergodic theory, etc.
Cui, J.; Hong, J. Wellposedness and regularity estimate for stochastic Cahn--Hilliard equation with unbounded noise diffusion SPDEs: Analysis and Computations. (2022), https://doi.org/10.1007/s40072-022-00272-8
Cui, J.; Dieci, L.; Zhou, H. A continuation multiple shooting method for Wasserstein geodesic equation SIAM J. Sci. Comput. 44 (2022), no. 5, A2918-A2943. GitHub
Cui, J.; Hong, J.; Sheng, D. Density function of numerical solution of splitting AVF scheme for stochastic Langevin equation. . Math. Comp. 91 (2022), no. 337, 2283-2333.
Chen, C. ; Cui, J.; Hong, J.; Sheng, D. Accelerated Exponential Euler Scheme for Stochastic Heat Equation: Convergence rate of Densities. IMA J. Numer. Anal. https://doi.org/10.1093/imanum/drac011
Cui, J.; Dieci, L.; Zhou, H. Time Discretizations of Wasserstein-Hamiltonian Flows. Math. Comp. 91 (2022), no. 335, 1019-1075.
Cui, J.; Hong, J.; Sun, L. Strong convergence of full discretization for stochastic Cahn-Hilliard equation driven by additive noise. SIAM J. Numer. Anal. 59 (2021), no. 6, 2866-2899.
Cui, J.; Liu S.; Zhou, H. What is a stochastic Hamiltonian process on finite graph? An optimal transport answer. J. Differential Equations 305 (2021), 428-457.
Cui, J.; Hong, J.; Sun, L. Weak convergence and invariant measure of a full discretization for parabolic SPDEs with non-globally Lipschitz coefficients. Stochastic Process. Appl. 134 (2021), 55-93.
Cui, J.; Hong, J. Absolute continuity and numerical approximation of stochastic Cahn-Hilliard equation with unbounded noise diffusion. J. Differential Equations 269 (2020), no. 11, 10143-0180.
Cohen, D.; Cui, J.; Hong, J.; Sun, L. Exponential integrators for stochastic Maxwell's equations driven by Ito noise. J. Comput. Phys. 410 (2020), 109382, 21 pp.
Cui, J.; Hong, J.; Sun, L. On global existence and blow-up for damped stochastic nonlinear Schrodinger equation. Discrete Contin. Dyn. Syst. Ser. B 24 (2019), no. 12, 6837-6854.
Brehier, C. E.; Cui, J.; Hong, J. Strong convergence rates of semidiscrete splitting approximations for the stochastic Allen-Cahn equation. IMA J. Numer. Anal. 39 (2019), no. 4, 2096-2134.
Cui, J.; Hong, J. Strong and weak convergence rates of a spatial approximation for stochastic partial differential equation with one-sided Lipschitz coefficient. SIAM J. Numer. Anal. 57 (2019), no. 4, 1815-1841.
Cui, J.; Hong, J.; Liu, Z.; Zhou, W. Strong convergence rate of splitting schemes for stochastic nonlinear Schrodinger equations. J. Differential Equations 266 (2019), no. 9, 5625-5663.
Cui, J.; Hong, J. Analysis of a splitting scheme for damped stochastic nonlinear Schrodinger equation with multiplicative noise. SIAM J. Numer. Anal. 56 (2018), no. 4, 2045-2069.
Niu, X.; Cui, J.; Hong, J.; Liu, Z. Explicit pseudo-symplectic methods for stochastic Hamiltonian systems. BIT 58 (2018), no. 1, 163-178.
Cui, J.; Hong, J.; Liu, Z. Strong convergence rate of finite difference approximations for stochastic cubic Schrodinger equations. J. Differential Equations 263 (2017), no. 7, 3687-3713.
Cui, J.; Hong, J.; Liu, Z.; Zhou, W. Stochastic symplectic and multi-symplectic methods for nonlinear Schrodinger equation with white noise dispersion. J. Comput. Phys. 342 (2017), 267-285.
Cui, J.; Liu, Z.; Miao, L.; Wang, X. Holder continuity for parabolic Anderson equation with non-Gaussian noise. J. Math. Anal. Appl. 441 (2016), no. 2, 684-691.
Cui, J.; Liu, S.; Zhou, H. Optimal control for stochastic nonlinear Schrodinger equation on graph arXiv2209.05346
Cui, J.; Hong, J.; Sun, L. Semi-implicit energy-preserving numerical schemes for stochastic wave equation via SAV approach arXiv2208.13394
Brehier, C. E.; Cui, J.; Wang, X. Weak error estimates of fully-discrete schemes for the stochastic Cahn-Hilliard equation arXiv:2207.09266
Cui, J.; Liu, S.; Zhou, H. Wasserstein Hamiltonian flow with common noise on graph arXiv:2204.01185
Cui, J. Explicit Numerical Methods for High Dimensional Stochastic Nonlinear Schrodinger Equation: Divergence, Regularity and Convergence arXiv:2112.10177
Cui, J.; Liu, S.; Zhou, H. Stochastic Wasserstein Hamiltonian Flows arXiv:2111.15163
Cui, J.; Hong, J.; Sun, L. Structure-preserving splitting methods for stochastic logarithmic Schrodinger equation via regularized energy approximation arXiv:2111.04402
Cui, J.; Sun, L. Stochastic logarithmic Schrodinger equations: energy regularized approach arXiv:2102.12607
Cui, J.; Hong, J.; Ji, L.; Sun, L. Energy-preserving exponential integrable numerical method for stochastic cubic wave equation with additive noise arXiv:1909.00575
SIAM Journal on Numerical Analysis;
Numerische Mathematik;
Annals of Applied Probability;
Stochastic Process. Appl.;
Journal of Differential Equations;
IMA Journal of Numerical Analysis;
SIAM Journal on Control and Optimization;
SPDEs: Analysis and Computations;
Communications in Mathematical Sciences;
Applied Numerical Mathematics;
Journal of Computational Mathematics;
Zeitschrift fur angewandte Mathematik und Physik;
Discrete and Continuous Dynamical Systems Series S;
Acta Mathematica Scientia;
Computers and Mathematics with Applications;
Communications on Pure and Applied Analysis;
International Journal of Numerical Analysis and Modeling;
CSIAM Transactions on Applied Mathematics;
J. Integral Equations Appl.; Results Appl. Math.;
Advances in Applied Mathematics and Mechanics;
Journal of Theoretical Probability;
AIMS Mathematics;
...
etc.