Convergence analysis for particle methods for one-dimensional vlasov-poisson systems

In this thesis, we first review the existence and uniqueness theory for one-dimensional Vlasov-Poisson systems. Then we provide a mathematical analysis of particle methods and give a proof of the convergence of the Hamiltonian trajectories of the mollified fields to those associated with the exact fields. We next consider the incorporation of time discretization methods into the calculation of the trajectories and prove a stability result which examines the sensitivity of the mollified fields with respect to charge positions. Finally, we compare particle methods to finite-difference methods for numerical experiments that specifically use initial data that lead to Landau damping and two-stream instability effects.