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We introduce a new class of arbitrary-order exponential time differencingmethods based on spectral deferred correction (ETDSDC) and describe a simpleprocedure for initializing the requisite matrix functions. We compare thestability and accuracy properties of our ETDSDC meth- ods to those of anexisting implicit-explicit spectral deferred correction scheme (IMEXSDC). Wefind that ETDSDC methods have larger accuracy regions and comparable stabilityregions. We conduct numerical experiments to compare ETD and IMEX spectraldeferred correction schemes against a competing fourth-order ETD Runge-Kuttascheme. We find that high-order ETDSDC schemes are the most efficient in termsof function evaluations and overall speed when solving partial differentialequations to high accuracy. Our results suggest that high-order ETDSDC schemesare well-suited to work in conjunction with spectral spatial methods or otherhigh-order spatial discritizations. Addi- tionally, ETDSDC schemes appear to beimmune to severe order reduction, a problem which affects other ETD and IMEXschemes, including IMEXSDC.

A Class of Exponential Integrators Based on Spectral Deferred Correction