# Gray-Scott Reaction-Diffusion Cell with an Applied Electric Field

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Consider the Gray–Scott reaction-diffusion cell with an applied electric field. The governing equations and boundary and initial conditions are:

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Contributed by: Housam Binousand Brian G. Higgins (June 2013)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

In the discrete Chebyshev–Gauss–Lobatto case, the interior points are given by . These points are the extrema of the Chebyshev polynomials of the first kind, .

The Chebyshev derivative matrix at the quadrature points is an matrix given by

, , for , and for and ,

where for and .

The matrix is then used as follows: and , where is a vector formed by evaluating at , , and and are the approximations of and at the .

Reference

[1] P. Moin, *Fundamentals of Engineering Numerical Analysis*, Cambridge, UK: Cambridge University Press, 2001.

[2] L. N. Trefethen, *Spectral Methods in Matlab*, Philadelphia: SIAM, 2000.

[3] A. W. Thornton and T. R. Marchant, "Semi-analytical solutions for a Gray–Scott reaction–diffusion cell with an applied electric field," *Chemical Engineering Science*, 63(2), 2008 pp. 495–502. DOI: 10.1016/j.ces.2007.10.001 .

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