Exponential integrators for time–fractional partial differential equations

Time–fractional partial differential equations can be numerically solved by first discretizing with respect to the spatial derivatives and hence applying a time–step integrator. An exponential integrator for fractional differential equations is proposed to overcome the stability issues due to the stiffness in the resulting semi–discrete system. Convergence properties and the main implementation issues are studied. The advantages of the proposed method are illustrated by means of some test problems.