Solving systems of IVPs with discontinuous derivatives—Numerical experiments

We deal in this paper with solving IVPs with singular right-hand side. We consider two recent algorithms of Kacewicz and Przybyłowicz for solving systems of IVPs with right-hand side functions which are globally Lipschitz continuous and piecewise rr-smooth with piecewise Hölder rrth partial derivatives with Hölder exponent ρ∈(0,1]ρ∈(0,1]. The singularity hypersurface is defined by the zeros of an unknown event function. We run several numerical experiments to verify the theoretical results of Kacewicz and Przybyłowicz. Our tests confirm that the bounds on the error O(n−(r+ρ))O(n−(r+ρ)) can be achieved with O(n)O(n) function evaluations, where nn is a number of discretization points.