A semi-implicit formulation of the method of spectral deferred corrections (SISDC)
for ordinary differential equations with both stiff and non-stiff terms is presented. Several modifications
and variations to the original spectral deferred corrections method by Dutt, Greengard,
and Rokhlin concerning the choice of integration points and the form of the correction iteration
are presented. The stability and accuracy of the resulting ODE methods for both stiff and nonstiff
problems are explored analytically and numerically. The SISDC methods are intended to be
combined with the method of lines approach to yield a flexible framework for creating higher-order
semi-implicit methods for partial differential equations. A discussion and numerical examples of
the SISDC method applied to advection-diffusion type equations are included. The results suggest
that higher-order SISDC methods are a competitive alternative to existing Runge-Kutta and linear
multistep methods based on the accuracy per function evaluation.