A Lifting Method for Krause’s Consensus Model (Communications in Mathematical Research, 2021)
In this work, we aim to show how to solve the continuous-timeand continuous-space Krause model by using high-order finite difference (FD)schemes. Since the considered model admits solutions with $δ$-singularities, theFD method cannot be applied directly. To deal with the annoying $δ$-singularities, we propose to lift the solution space by introducing a splitting method, suchthat the $δ$-singularities in one spatial direction become step functions with discontinuities. Thus the traditional shock-capturing FD schemes can be applieddirectly. In particular, we focus on the two-dimensional case and apply a fifth-order weighted nonlinear compact scheme (WCNS) to illustrate the validityof the proposed method. Some technical details for implementation are alsopresented. Numerical results show that the proposed method can capture $δ$-singularities well, and the obtained number of delta peaks agrees with the theoretical prediction in the literature.