Contributed Talk
A computationally efficient strategy for time-fractional diffusion-reaction equations
University of Bari Aldo Moro, Italy
Abstract
The numerical treatment of diffusion-reaction equations with time-fractional derivatives is often a very challenging task from the computational point of view.
The non-locality of fractional-order operators, and the need of considering a persistent memory in the numerical computation, usually result in an extremely
demanding need of storage memory and computational resources. In this work [1] we devise a computationally efficient strategy to perform numerical simulations
in an acceptable time and with a reasonable memory occupation. An ImEx product-integration rule is coupled with a kernel compression scheme allowing
to approximate the non-local problem in a sequence of local problems. To optimize the computational task involved by solving the large number of local problems,
we adopt a matrix form for the semidiscretized problem so as to require the solution of Sylvester equations only with small matrices. Results about the accuracy
of the proposed scheme are presented together with numerical experiments showing the efficiency of this strategy from the computational point of view.
References
[1] R.Garrappa, M.Popolizio, A computationally efficient strategy for time-fractional diffusion-reaction equations, Computers & Mathematics with Applications, 2021.
Joint work with Marina Popolizio, Politecnico di Bari, Italy