Summary
Ordinary Differential Equations with discontinuities in the state variables require a differential inclusion formulation to guarantee existence [8]. From this formulation a high accuracy method for solving such initial value problems is developed which can give any order of accuracy and “tracks” the discontinuities. The method uses an “active set” approach, and determines appropriate active sets from solutions to Linear Complementarity Problems. Convergence results are established under some non-degeneracy assumptions. The method has been implemented, and results compare favourably with previously published methods [7, 21].
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Stewart, D. A high accuracy method for solving ODEs with discontinuous right-hand side. Numer. Math. 58, 299–328 (1990). https://doi.org/10.1007/BF01385627
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DOI: https://doi.org/10.1007/BF01385627