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

Abstract. In this article we analyze a fully discrete numerical approximation to a time depen-dent 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.