My research interests include energy minimization problems and related gradient flows, collective dynamics, numerical methods for kinetic and hyperbolic problems, and uncertainty quantification.
 Sigal Gottlieb, Zachary Grant, Jingwei Hu and Ruiwen Shu, High order unconditionally strong stability preserving multi-derivative implicit and IMEX Runge-Kutta methods with asymptotic preserving properties, submitted.
 Douglas Hardin, Edward Saff, Ruiwen Shu and Eitan Tadmor, Dynamics of particles on a curve with pairwise hyper-singular repulsion, submitted.
 Ruiwen Shu and Eitan Tadmor, Newtonian repulsion and radial confinement: convergence towards steady state, submitted.
 Ruiwen Shu, Tightness of radially-symmetric solutions to 2D aggregation-diffusion equations with weak interaction forces, submitted.
 Ruiwen Shu, Equilibration of aggregation-diffusion equations with weak interaction forces, submitted. (See an updated version)
 Jingwei Hu and Ruiwen Shu, On the uniform accuracy of implicit-explicit backward differentiation formulas (IMEX-BDF) for stiff hyperbolic relaxation systems and kinetic equations, Mathematics of Computation, 90 (2021), 641-670.
 Shi Jin and Ruiwen Shu, Collective dynamics of opposing groups with stochastic communication, Vietnam Journal of Mathematics, 2020: 1-18.
 Ruiwen Shu and Eitan Tadmor, Anticipation breeds alignment, submitted.
 Jingwei Hu, Shi Jin and Ruiwen Shu, On stochastic Galerkin approximation of the nonlinear Boltzmann equation with uncertainty in the ﬂuid regime, J. Comput. Phys., 397: 108838, 2019.
 Ruiwen Shu and Eitan Tadmor, Flocking hydrodynamics with external potentials, Archive for Rational Mechanics and Analysis, 2020: 1-35.
 Shi Jin and Ruiwen Shu, A study of hyperbolicity of kinetic stochastic Galerkin system for the isentropic Euler equations with uncertainty, Chinese Annals of Mathematics, Series B, 40(5), 765-780, 2019.
 Jingwei Hu and Ruiwen Shu, A second-order asymptotic-preserving and positivity-preserving exponential Runge-Kutta method for a class of stiff kinetic equations, SIAM Multiscale Model. Simul., 17(4): 1123-1146, 2019.
 Ruiwen Shu and Shi Jin, A study of Landau damping with random initial inputs, J. Differ. Equat., 266(4), 1922-1945, 2019.
 Jingwei Hu, Ruiwen Shu and Xiangxiong Zhang, Asymptotic-preserving and positivity-preserving implicit-explicit schemes for the stiff BGK equation, SIAM J. Numer. Anal., 56(2), 942-973, 2018.
 Qin Li, Jian-Guo Liu and Ruiwen Shu, Sensitivity analysis of Burgers’ equation with shocks, SIAM/ASA J. Uncertainty Quantification, to appear.
 Qin Li, Ruiwen Shu and Li Wang, A new numerical approach to inverse transport equation with error analysis, SIAM J. Numer. Anal., 56(6), 3358-3385, 2018.
 Ruiwen Shu and Shi Jin, Uniform regularity in the random space and spectral accuracy of the stochastic Galerkin method for a kinetic-fluid two-phase flow model with random initial inputs in the light particle regime, ESAIM Math. Model. Numer. Anal., 52(5), 1651-1678, 2018.
 Jingwei Hu, Shi Jin and Ruiwen Shu, A stochastic Galerkin method for the Fokker-Planck-Landau equation with random uncertainties, Proc. 16th Int’l Conf. on Hyperbolic Problems, pp. 1-19, 2016.
 Ruiwen Shu, Jingwei Hu and Shi Jin, A Stochastic Galerkin Method for the Boltzmann Equation with multi-dimensional random inputs using sparse wavelet bases, Numer. Math. Theor. Meth. Appl. (NMTMA) 10, 465-488, 2017. (A special issue in honor of the 80th birthday of Prof. Zhenhuan Teng)
 Shi Jin and Ruiwen Shu, A stochastic Asymptotic-Preserving scheme for a kinetic-fluid model for disperse two-phase flows with uncertainty, J. Comput. Phys., 335, 905-924, 2017.