A computationally efficient strategy for time-fractional diffusion-reaction equations

An efficient strategy for the numerical solution of time-fractional diffusion-reaction problems is devised. A standard finite difference discretization of the space derivative is initially applied which results in a linear stiff term. Then a rectangular product-integration (PI) rule is implemented in an implicit-explicit (IMEX) framework in order to implicitly treat this linear stiff term and handle in an explicit way the non-linear, and usually non-stiff, term.