A Projection Method For A Class Of Convolution Complementarity Problems

Complementarity problems are a mathematical model,which are widely used in many areas,such as economy,engineering and so on.They also have close connection with lots of mathematics branches.Convolution complementarity problems,as a kind of infinite dimensional complementarity problems,are often used for describing linear complementarity systems,switching systems,variable structure systems,discontinuous ODEs,elastic body impact problems and other systems,so they have high research value and practical significance.We introduced two kinds of numerical methods for solving convolution complementarity problems,and proved their numerical behavior by presenting some numerical results.The two methods both approach the exact solution by piecewise constant functions.The first method defines the complementarity conditions at gird points of the mesh based on time-step thought to achieve a series of finite dimensional complementarity problems.By solving these finite dimensional complementarity problems,we can get the approximate solution of convolution complementarity problems.While the second method extended the thought of gradient-projection method to convolution complementarity problems.With two kinds of different methods,we analyzed and compared the numerical results for Tacoma suspension bridge problem and Parabolic Signorini problem.The experiment showed that both two methods are effective when they were used for convolution complementarity problems satisfying given assumptions and the rate of convergence with the time step is approximately linear.Besides,the rate of convergence of the second method was a little faster than the first method.