This work is dedicated to the memory of Donato Trigiante who has been the first teacher of Numerical Analysis of the second author. The authors remember Donato as a generous teacher, always ready to discuss with his students, able to give them profound and interesting suggestions. Here, we present a survey of numerical methods for differential systems with discontinuous right hand side. In particular, we will review methods where the discontinuities are detected by using an event function (so-called event driven methods) and methods where the discontinuities are located by controlling the local errors (so-called time-stepping methods). Particular attention will be devoted to discontinuous systems of Filippov's type where sliding behavior on the discontinuity surface is allowed. © 2012 Elsevier B.V. All rights reserved.
Dieci, L., & Lopez, L. (2012). A survey of numerical methods for IVPs of ODEs with discontinuous right-hand side. Journal of Computational and Applied Mathematics, 236(16), 3967–3991. https://doi.org/10.1016/j.cam.2012.02.011