SciCADE 2013
International Conference on Scientific Computation and Differential Equations
September 16-20, 2013, Valladolid (Spain)

Invited Talk

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Numerical solution of fractional differential equations with discontinuous right-hand side

R. Garrappa

Recently, a growing interest has been shown in the study of fractional differential equations (FDEs) with discontinuous right-hand side and their applications in sliding mode control. This talk concerns with the numerical solution of discontinuous FDEs; after studying, for some test problems, the finite-time convergence of the true solution on the sliding surface, we describe two methods for FDEs obtained by generalizing, in different ways, the classical implicit Euler method. An interesting result allows to show that different methods derived from the same implicit Euler method behave in a different way when applied to discontinuous problems and just the method devised in the framework of the {fractional linear multistep methods} inherit the chattering-free character of the original method [1]. We focus the attention on this method, which allows finite-time stabilization on the sliding surface, study its main properties and present test problems.

[1] V. Acary and B. Brogliato, Implicit Euler numerical scheme and chat\-tering-free implementation of sliding mode systems, Systems & Control Letters, 59 (2010), pp. 284-293
[2] R. Garrappa, On some generalizations of the implicit Euler method for discontinuous fractional differential equations, Mathematics and Computers in Simulation, in print, doi:10.1016/j.matcom.2012.04.009

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