Exponential Time-stepping Method For Differential Affine Variational Inequalities

Differential affine variational inequalities is a hybrid problem consisting of an ordinary differential equation(ODE)and a linear complementarity problem(LCP).In this paper,we analyze the existence,uniqueness and perturbation of solutions to differential affine variational inequalities,propose a exponential time-stepping methods and analyze its convergence.The proposed method uses exponential integrator to discretize the ODE and solves the LCPs at the discretized time points,it performs much better than the standard time-stepping method.Finally,we use numerical experiments to verify the effectiveness of the exponential time-stepping method.