Numerical Approximation of a Time Dependent, Nonlinear, Space-Fractional Diffusion Equation

Authors:
Vincent J. Ervin;Norbert Heuer;John Paul Roop
Affiliations:
-;-;-
Venue:
SIAM Journal on Numerical Analysis
Year:
2007

Citing 0
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Abstract

In this article we analyze a fully discrete numerical approximation to a time dependent fractional order diffusion equation which contains a nonlocal quadratic nonlinearity. The analysis is performed for a general fractional order diffusion operator. The nonlinear 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.