12 citations · 26 across the 9 of their papers we have counts for
7 papers · 1 filter
Maximum bound principles for a class of semilinear parabolic equations and exponential time differencing schemes
Qiang Du, Lili Ju, Xiao Li +1
The ubiquity of semilinear parabolic equations has been illustrated in their numerous applications ranging from physics, biology, to materials and social sciences. In this paper, w…
Nonlocal-in-time dynamics and crossover of diffusive regimes
Qiang Du, Zhi Zhou
We study a simple nonlocal-in-time dynamic system proposed for the effective modeling of complex diffusive regimes in heterogeneous media. We present its solutions and their common…
Numerical methods for nonlocal and fractional models
Marta D'Elia, Qiang Du, Christian Glusa +3
Partial differential equations (PDEs) are used, with huge success, to model phenomena arising across all scientific and engineering disciplines. However, across an equally wide swa…
Discovery of Dynamics Using Linear Multistep Methods
Rachael Keller, Qiang Du
Linear multistep methods (LMMs) are popular time discretization techniques for the numerical solution of differential equations. Traditionally they are applied to solve for the sta…
Multiscale Modeling, Homogenization and Nonlocal Effects: Mathematical and Computational Issues
Qiang Du, Bjorn Engquist, Xiaochuan Tian
In this work, we review the connection between the subjects of homogenization and nonlocal modeling and discuss the relevant computational issues. By further exploring this connect…
Time-Fractional Allen-Cahn Equations: Analysis and Numerical Methods
Qiang Du, Jiang Yang, Zhi Zhou
In this work, we consider a time-fractional Allen-Cahn equation, where the conventional first order time derivative is replaced by a Caputo fractional derivative with order $α\in(0…