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Generalized integrating factor methods for stiff PDEs. (English) Zbl 1063.65097
Summary: The integrating factor (IF) method for numerical integration of stiff nonlinear partial differential equations (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 ETD Runge-Kutta method with improved accuracy. The methods considered are compared in several numerical examples.

MSC:
65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
35F25 Initial value problems for nonlinear first-order PDEs
65L05 Numerical methods for initial value problems
Software:
Matlab; RODAS
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