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A new mesh selection strategy with stiffness detection for explicit Runge-Kutta methods. (English) Zbl 1338.68293
Summary: In this paper, we develop a new mesh selection strategy based on the computation of some conditioning parameters which allows to give information about the conditioning and the stiffness of the problem. The reliability of the proposed algorithm is demonstrated by some numerical experiments. We observe that “when an initial value problem is run on a computer, the results may appear plausible even if they are unreliable because of some unrecognized numerical instability” [R. H. Miller, J. Comput. Phys. 2, 1–7 (1967; Zbl 0158.15501)]. The additional information about the behavior of the numerical solution provided by the new mesh selection algorithm are, therefore, of great interest for potential users of a numerical computer code.

68W25 Approximation algorithms
Full Text: DOI
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