TY - JOUR
T1 - A Lifting Method for Krause’s Consensus Model
AU - Guo , Ningbo
AU - Chen , Yaming
AU - Deng , Xiaogang
JO - Communications in Mathematical Research 
VL - 1
SP - 52
EP - 61
PY - 2021
DA - 2021/11
SN - 38
DO - http://doi.org/10.4208/cmr.2021-0053
UR - https://global-sci.org/intro/article_detail/cmr/19956.html
KW - Krause’s consensus model, lifting method, finite difference method, $δ$-singularities.
AB - <p style="text-align: justify;">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 $δ$-singularities, 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 discontinuities. 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 theoretical prediction in the literature.</p>