Runge-Kutta Time-Stepping Method For Linear Complementarity Systems

The linear complementarity system(LCS)is a coupled system of ordinary differ-ential equation and a linear complementarity problem(LCP).Existing numerical meth-ods possess only convergence of one order for the best case.In this paper we present a Runge-Kutta time-stepping method,we show its convergence.Besides we propose a numerical method for finding some critical time points,which give the subintervals(called as smooth pieces)in which the solution of the LCS is smooth.We suggest piecewise applying the Runge-Kutta time-stepping method inside each smooth pieces,this gives our Runge-Kutta Scheme based piecewise integration method,for which one can expect high convergence order.We perform numerical experiments to support our arguments.