Numerical approximation of a time dependent, nonlinear, space-fractional
order diffusion equation
Vincent J. Ervin, Norbert Heuer and John Paul Roop
SIAM J. Numer. Anal. 45 (2), 572-591, 2007.
In this article we analyze a fully discrete numerical approximation to a time dependent fractional
order diffusion equation which contains a non-local, quadratic non-linearity. The analysis is
performed for a general fractional order diffusion operator. The non-linear term studied is a
product of the unknown function and a convolution operator of order 0. Convergence of the
approximation and a priori error estimates are given. Numerical computations are included which
confirm the theoretical predictions.