A Lifting Method for Krause's Consensus Model

In this work,we aim to show how to solve the continuous-time and continuous-space Krause model by using high-order finite difference(FD)schemes.Since the considered model admits solutions with δ-singularities,the FD method cannot be applied directly.To deal with the annoying δ-singulariti-es,we propose to lift the solution space by introducing a splitting method,such that the δ-singularities in one spatial direction become step functions with dis-continuities.Thus the traditional shock-capturing FD schemes can be applied directly.In particular,we focus on the two-dimensional case and apply a fifth-order weighted nonlinear compact scheme(WCNS)to illustrate the validity of the proposed method.Some technical details for implementation are also presented.Numerical results show that the proposed method can capture δ-singularities well,and the obtained number of delta peaks agrees with the the-oretical prediction in the literature.