ETD.jl

Exploratory analysis of exponential time differencing

This program is based on a joint COMS 7300 final project (Spring 2017) by Toheeb Biala and Ashlin Harris. It uses the exponential time differencing (ETD) scheme to obtain solutions to the fractional reaction diffusion equation. Space derivatives are discretized using the Matrix Transfer Technique (MTT) developed by Ilic et al.¹. For the time dimension, we use the ETD schemes given by Kleefeld, Khaliq, and Wade².

Footnotes

1. Ilic, M.; Liu, F.; Turner, I. & Anh, V. "Numerical approximation of a fractional-in-space diffusion equation (II) - with nonhomogenous boundary conditions" Fractional Calculus and Applied Analysis, 2006. ↩

2. Kleefeld, B.; Khaliq, A. & Wade, B. "An ETD Crank-Nicolson method for reaction-diffusion systems" Numerical Methods for Partial Differential Equations, Wiley Online Library, 2012, 28, 1309-1335 ↩