Convergence of a linearly transformed particle method for aggregation equations
This work offers rigorous convergence guarantees for a numerical method used in simulating aggregation phenomena, which is important for researchers in computational mathematics and physics.
The paper provides convergence estimates for a linearly transformed particle method applied to aggregation equations with smooth or singular interaction forces, proving error bounds in various norms.
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 $L^1$ and $L^\infty$ 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 $L^1 \cap L^p$ norm.