A high accuracy method for solving ODEs with discontinuous right-hand side (Q908664)

Ordinary differential equations with discontinuities in the right-hand side in the state variables require a differential inclusion formulation to guarantee the existence of solutions. Using this formulation a high accuracy method for solving initial value problems (which can attain arbitrary order) is developed which ``tracks'' the discontinuities. The method is an ``active set'' approach and determines appropriate active sets of discontinuities from solutions to linear complementarity problems. Convergence results are established under non-degeneracy conditions. The method has been implemented, and the results compare favourably with previously published methods.