Sliding Motion in Filippov Differential Systems: Theoretical Results and a Computational Approach
SIAM Journal on Numerical Analysis
A survey of numerical methods for IVPs of ODEs with discontinuous right-hand side
Journal of Computational and Applied Mathematics
Original article: Rosenbrock-type methods applied to discontinuous differential systems
Mathematics and Computers in Simulation
Optimal solution of a class of non-autonomous initial-value problems with unknown singularities
Journal of Computational and Applied Mathematics
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We consider the numerical integration of discontinuous differential systems of ODEs of the type: x^'=f"1(x) when h(x)0, and with f"1f"2 for x@?@S, where @S:={x:h(x)=0} is a smooth co-dimension one discontinuity surface. Often, f"1 and f"2 are defined on the whole space, but there are applications where f"1 is not defined above @S and f"2 is not defined below @S. For this reason, we consider explicit Runge-Kutta methods which do not evaluate f"1 above @S (respectively, f"2 below @S). We exemplify our approach with subdiagonal explicit Runge-Kutta methods of order up to 4. We restrict attention only to integration up to the point where a trajectory reaches @S.