Exponential integrators for time–fractional partial differential equations
Dipartimento di Matematica, Università degli Studi di Bari, via E. Orabona 4, 70125 Bari, Italy
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Received: 3 June 2013
Revised: 6 August 2013
Published online: 7 October 2013
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.
© EDP Sciences, Springer-Verlag, 2013