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in’t Hout, Karel J.

On the contractivity of implicit-explicit linear multistep methods. (English) Zbl 1001.65090

Appl. Numer. Math. 42, No. 1-3, 201-212 (2002).
Stability properties of implicit-explicit linear multistep methods (IMEX) are analyzed for the case of initial value problems for ordinary differential equations composed of stiff and nonstiff parts. In particular, the paper deals with contractivity and strong stability of the iterative process in the case of the linear autonomous test problem and an Euclidean norm. Several proposition and theorems concerning the contractivity and strong stability of IMEX are proved. The situation where the contractivity region is replaced by the larger stability region, is also considered.
Reviewer: Dana Petcu (Timişoara)

Cited in 9 Documents

MSC:

65L20 Stability and convergence of numerical methods for ordinary differential equations
65L05 Numerical methods for initial value problems involving ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations

Keywords:

implicit-explicit linear multistep methods; stability; contractivity; stiff systems; numerical examples; initial value problems
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References:

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