We study a linearly transformed particle method for the aggregation equation with smooth or singular interaction forces. For the smooth interaction forces, we provide convergence estimates in L1 and L∞ norms depending on the regularity of the initial data. Moreover, we give convergence estimates in bounded Lipschitz distance for measure valued solutions. For singular interaction forces, we establish the convergence of the error between the approximated and exact flows up to the existence time of the solutions in L1∩ Lp norm.
Bibliographical noteFunding Information:
Acknowledgements JAC was partially supported by the EPSRC Grant Number EP/P031587/1 and from the Royal Society by a Wolfson Research Merit Award. YPC was supported by National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (Nos. 2017R1C1B2012918 and 2017R1A4A1014735). JAC and YPC were supported by EPSRC grant with Reference EP/K008404/1. This work was partially done when FC was visiting Imperial College funded by the EPSRC EP/I019111/1 (platform grant).
© 2018, The Author(s).
All Science Journal Classification (ASJC) codes
- Computational Mathematics
- Applied Mathematics