A high order time splitting method based on integral deferred correction for semi-Lagrangian Vlasov simulations

Andrew Christlieb, Wei Guo, Maureen Morton, Jing Mei Qiu

Research output: Contribution to journalArticlepeer-review

36 Scopus citations


Semi-Lagrangian schemes with various splitting methods, and with different reconstruction/interpolation strategies have been applied to kinetic simulations. For example, the order of spatial accuracy of the algorithms proposed in Qiu and Christlieb (2010) [29] is very high (as high as ninth order). However, the temporal error is dominated by the operator splitting error, which is second order for Strang splitting. It is therefore important to overcome such low order splitting error, in order to have numerical algorithms that achieve higher orders of accuracy in both space and time. In this paper, we propose to use the integral deferred correction (IDC) method to reduce the splitting error. Specifically, the temporal order accuracy is 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 simulations in the vorticity stream-function formulation. We show numerically that the IDC procedure can automatically increase the order of accuracy in time. We also investigate numerical stability of the proposed algorithm via performing Fourier analysis to a linear model problem.

Original languageEnglish
Pages (from-to)7-27
Number of pages21
JournalJournal of Computational Physics
StatePublished - Jun 15 2014


  • Guiding center model
  • Integral deferred correction
  • Operator/dimensional splitting
  • Semi-Lagrangian method
  • Vlasov-Poisson system
  • WENO reconstruction


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