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On the stability of semi-implicit methods for ordinary differential equations

Bader, Georg
Lubich, Christian
Published in BIT Numerical Mathematics. 1982, vol. 22, no. 2, p. 211-232
Abstract The aim of this paper is to analyze the stability properties of semi-implicit methods (such as Rosenbrock methods, W-methods, and semi-implicit extrapolation methods) for nonlinear stiff systems of differential equations. Properties of the error growth function are studied. Further, conditions for the parameters of a semi-implicit method are given, which imply that the method produces contractive numerical solutions over a large class of nonlinear problems for sufficiently small h. The restriction on the stepsize, however, does not depend on the stiffness of the differential equation. Finally, the presented theory is applied to the extrapolation method based on the semi-implicit mid-point rule.
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HAIRER, Ernst, BADER, Georg, LUBICH, Christian. On the stability of semi-implicit methods for ordinary differential equations. In: BIT Numerical Mathematics, 1982, vol. 22, n° 2, p. 211-232. doi: 10.1007/BF01944478

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Deposited on : 2010-11-15

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