27 citations · 31 across the 7 of their papers we have counts for
7 papers
A second-order accurate, original energy dissipative numerical scheme for chemotaxis and its convergence analysis
Jie Ding, Cheng Wang, Shenggao Zhou
This paper proposes a second-order accurate numerical scheme for the Patlak-Keller-Segel system with various mobilities for the description of chemotaxis. Formulated in a variation…
Second-order, Positive, and Unconditional Energy Dissipative Scheme for Modified Poisson-Nernst-Planck Equations
Jie Ding, Shenggao Zhou
First-order energy dissipative schemes in time are available in literature for the Poisson-Nernst-Planck (PNP) equations, but second-order ones are still in lack. This work propose…
Asymptotic behaviour of a conservative reaction-diffusion system associated with a Markov process algebra model
Jie Ding, Ruiming Ma, Zhigui Lin +1
This paper demonstrates a lower and upper solution method to investigate the asymptotic behaviour of the conservative reaction-diffusion systems associated with Markovian process a…
Convergence Analysis of Structure-Preserving Numerical Methods Based on Slotboom Transformation for the Poisson--Nernst--Planck Equations
Jie Ding, Cheng Wang, Shenggao Zhou
The analysis of structure-preserving numerical methods for the Poisson--Nernst--Planck (PNP) system has attracted growing interests in recent years. In this work, we provide an opt…
Hysteresis and Linear Stability Analysis on Multiple Steady-State Solutions to the Poisson--Nernst--Planck equations with Steric Interactions
Jie Ding, Hui Sun, Shenggao Zhou
In this work, we numerically study linear stability of multiple steady-state solutions to a type of steric Poisson--Nernst--Planck (PNP) equations with Dirichlet boundary condition…
Structure-Preserving and Efficient Numerical Methods for Ion Transport
Jie Ding, Zhongming Wang, Shenggao Zhou
Ion transport, often described by the Poisson--Nernst--Planck (PNP) equations, is ubiquitous in electrochemical devices and many biological processes of significance. In this work,…
Computational Study on Hysteresis of Ion Channels: Multiple Solutions to Steady-State Poisson--Nernst--Planck Equations
Jie Ding, Hui Sun, Zhongming Wang +1
The steady-state Poisson-Nernst-Planck (ssPNP) equations are an effective model for the description of ionic transport in ion channels. It is observed that an ion channel exhibits…