Generalized integrating factor methods for stiff PDEs

The integrating factor (IF) method for numerical integration of stiff nonlinear PDEs has the disadvantage of producing large error coefficients when the linear term has large norm. We propose a generalization of the IF method, and in particular construct multistep-type methods with several orders of magnitude improved accuracy. We also consider exponential time differencing (ETD) methods, and point out connections with a particular application of the commutator-free Lie group methods. We present a new fourth order ETDRK method with improved accuracy. The methods considered are compared in several numerical examples.