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math.NA2025
A Conservative and Positivity-Preserving Discontinuous Galerkin Method for the Population Balance Equation
Ziyao Xu, Guanyang Liu, Yong-Tao Zhang
We develop a conservative, positivity-preserving discontinuous Galerkin (DG) method for the population balance equation (PBE), which models the distribution of particle numbers acr…
math.NA2025
Exponential Time Differencing Runge-Kutta Discontinuous Galerkin (ETD-RKDG) Methods for Nonlinear Degenerate Parabolic Equations
Ziyao Xu, Yong-Tao Zhang
In this paper, we study high-order exponential time differencing Runge-Kutta (ETD-RK) discontinuous Galerkin (DG) methods for nonlinear degenerate parabolic equations. This class o…
math.NA2025
Stability and Time-Step Constraints of Exponential Time Differencing Runge--Kutta Discontinuous Galerkin Methods for Advection-Diffusion Equations
Ziyao Xu, Zheng Sun, Yong-Tao Zhang
In this paper, we investigate the stability and time-step constraints for solving advection-diffusion equations using exponential time differencing (ETD) Runge-Kutta (RK) methods i…