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Convergence results for general linear methods on singular perturbation problems

Published in BIT Numerical Mathematics. 1993, vol. 33, no. 4, p. 670-686
Abstract Many numerical methods used to solve Ordinary Differential Equations, or Differential Algebraic Equations can be written as general linear methods. The B-convergence results for general linear methods are for algebraically stable methods, and therefore useless for nearly A-stable methods. The purpose of this paper is to show convergence for singular perturbation problems for the class of general linear methods without assuming A-stability.
Keywords Multistep Runge-Kutta methodEpsilon expansionSingular perturbation problemsDifferential-algebraic equations
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Other version: http://link.springer.com/10.1007/BF01990542
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SCHNEIDER, Stefan. Convergence results for general linear methods on singular perturbation problems. In: BIT Numerical Mathematics, 1993, vol. 33, n° 4, p. 670-686. https://archive-ouverte.unige.ch/unige:76259

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Deposited on : 2015-10-19

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