Numerical analysis of a system described by implicitly-defined ordinary differential equations containing numerous discontinuities

Standard error-controlled variable step size algorithms break down or become extremely inefficient when used to integrate small systems of ordinary differential equations subject to discontinuous definition. An efficient technique is presented for use in conjunction with a standard integration algorithm when the differential equations contain arbitrary discontinuities. The effectiveness of this technique is illustrated in the analysis of a structural model comprising a large, implicitly defined, ordinary differential set which is subject to numerous discontinuities occurring at arbitrary intervals.