Abstract:
Evolution equations containing fractional derivatives can provide suitable mathemati-
cal models for describing important physical phenomena. In this paper, we propose a
fast and accurate method for numerical solutions of space fractional reaction-diffusion
equations. The proposed method is based on a exponential integrator scheme in time
and the Fourier spectral method in space. The main advantages of this method are
that it yields a fully diagonal representation of the fractional operator, with increased
accuracy and efficiency, and a completely straightforward extension to high spatial di-
mensions. Although, in general, it is not obvious what role a high fractional derivative
can play and how to make use of arbitrarily high-order fractional derivatives, we in-
troduce them to describe fractional hyper-diffusions in reaction diffusion. The scheme
justified by a number of computational experiments, this includes two and three dimen-
sional partial differential equations. Numerical experiments are provided to validate
the effectiveness of the proposed approach.
