  We introduce a new class of arbitrary-order exponential time differencing
methods based on spectral deferred correction (ETDSDC) and describe a simple
procedure for initializing the requisite matrix functions. We compare the
stability and accuracy properties of our ETDSDC meth- ods to those of an
existing implicit-explicit spectral deferred correction scheme (IMEXSDC). We
find that ETDSDC methods have larger accuracy regions and comparable stability
regions. We conduct numerical experiments to compare ETD and IMEX spectral
deferred correction schemes against a competing fourth-order ETD Runge-Kutta
scheme. We find that high-order ETDSDC schemes are the most efficient in terms
of function evaluations and overall speed when solving partial differential
equations to high accuracy. Our results suggest that high-order ETDSDC schemes
are well-suited to work in conjunction with spectral spatial methods or other
high-order spatial discritizations. Addi- tionally, ETDSDC schemes appear to be
immune to severe order reduction, a problem which affects other ETD and IMEX
schemes, including IMEXSDC.
