Convergence analysis of Strang splitting for Vlasov-type equations
Lukas Einkemmer, Alexander Ostermann
TL;DR
This paper provides a rigorous second-order convergence analysis of the Strang splitting method for Vlasov-type equations, including the Vlasov-Poisson equation, supported by numerical experiments.
Contribution
It offers the first rigorous convergence proof of Strang splitting for Vlasov-type equations in an abstract setting, verifying second-order accuracy.
Findings
Second-order convergence of Strang splitting under suitable assumptions
Application to Vlasov-Poisson equation in 1+1 dimensions
Numerical experiments confirming theoretical results
Abstract
A rigorous convergence analysis of the Strang splitting algorithm for Vlasov-type equations in the setting of abstract evolution equations is provided. It is shown that under suitable assumptions the convergence is of second order in the time step \tau. As an example, it is verified that the Vlasov-Poisson equation in 1+1 dimensions fits into the framework of this analysis. Also, numerical experiments for the latter case are presented.
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