Abstract
Existing convergence concepts for the analysis of discretizations of nonlinear stiff problems suffer from considerable drawbacks. Our intention is to extend the convergence theory to a relevant class of nonlinear problems, where stiffness is axiomatically characterized in natural geometric terms.
Our results will be presented in a series of papers. In the present paper (Part I) we motivate the need for such an extension of the existing theory, and our approach is illustrated by means of a convergence argument for the Implicit Euler scheme.
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Auzinger, W., Frank, R. & Kirlinger, G. Extending convergence theory for nonlinear stiff problems part I. Bit Numer Math 36, 635–652 (1996). https://doi.org/10.1007/BF01733784
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DOI: https://doi.org/10.1007/BF01733784