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Semi-Lagrangian schemes with various splitting methods, and with differentreconstruction/interpolation strategies have been applied to kineticsimulations. For example, the order of spatial accuracy of the algorithmsproposed in {[Qiu and Christlieb, J. Comp. Phys., 2010]} is very high (as highas ninth order). However, the temporal error is dominated by the operatorsplitting error, which is second order for Strang splitting. It is thereforeimportant to overcome such low order splitting error, in order to havenumerical algorithms that achieve higher orders of accuracy in both space andtime. In this paper, we propose to use the integral deferred correction (IDC)method to reduce the splitting error. Specifically, the temporal order accuracyis increased by $r$ with each correction loop in the IDC framework, where$r=1,\,2$ for coupling the first order splitting and the Strang splitting,respectively. The proposed algorithm is applied to the Vlasov-Poisson system,the guiding center model, and two dimensional incompressible flow simulationsin the vorticity stream-function formulation. We show numerically that the IDCprocedure can automatically increase the order of accuracy in time. We alsoinvestigate numerical stability of the proposed algorithm via performingFourier analysis to a linear model problem.

A High Order Time Splitting Method Based on Integral Deferred Correction for Semi-Lagrangian Vlasov Simulations