Validated Interval Solution Of Initial Value Problem Of Linear Complementarity System

Linear complementarity problem plays a significant role in optimization theory,it has wide applications in engineering and economics.In this thesis we study the socalled linear complementarity system(LCS for short),which is coupled by a linear complementarity problem and an ordinary differential equation.For the initial value problem of the LCS,we investigate the computation of the validated solution.This is a time-dependent interval vector valued function.It provides the approximate solution of the LCS along with the error bound.The bound covers various errors arising in the numerical computation like the discretization error,the approximation error.With the help of roundoff error tracking software(like the Intlab),the bound covers all possible errors,so it can be called guaranteed.We also report numerical results to illustrate the properties of the validated solution.