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

Invited Talk

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Runge-Kutta methods for the numerical solution of discontinuous systems of Filipov's type

J.I. Montijano, M. Calvo and L. Rández

In this work we consider the numerical solution of initial value problems of ODEs with discontinuous right-hand side. In particular we are interested in the integration of Filipov's type systems where sliding behaviour on the discontinuity surface is allowed. We show how Runge-Kutta methods can be adapted to the solution of this class of problems, with the minimum information about the problem provided by the user. Some numerical experiments using the well known DOPRI5(4) scheme are presented.

[1] M. Calvo, J.I. Montijano and L. Rández, On the solution of discontinuous IVPs by adaptive Runge-Kutta codes, Numerical Algorithms, 33 (2003), pp. 163-182.
[2] L. Dieci and L. Lopez, A survey of numerical methods for IVPs of ODEs with discontinuous right-hand side, J. Comput. Appl. Math., 236 (2012), pp. 3967-3991.

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