  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, J. Comp. Phys., 2010]} 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.
