Energy-Conserving Numerical Scheme for the Poisson-Nerst-Plank Equations
Midwest Numerical Analysis Day 2016 (MWNADay 2016) / University of Lacrosse, Wisconsin
Midwest Numerical Analysis Day 2016 (MWNADay 2016)
University of Lacrosse, Wisconsin
April 23, 2016
The Poisson-Nernst-Planck equations are a system of nonlinear partial differential equations that describe flow of charged particles in solution. In particular, we are interested in the transport of ions in the biological membrane proteins (ion channels). This work is about the design of numerical schemes that preserve exactly (up to round off error) a discretized form of the energy dynamics of the system. We will present a scheme that achieves the conservation of energy law, and the numerical results.
Kabre, Julienne, "Energy-Conserving Numerical Scheme for the Poisson-Nerst-Plank Equations" (2016). Mathematics Faculty Proceedings, Presentations, Speeches, Lectures. 429.