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A new mesh selection strategy with stiffness detection for explicit Runge–Kutta methods

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  • Mazzia, Francesca
  • Nagy, A.M.

Abstract

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” (Miller, 1967) [23]. 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.

Suggested Citation

  • Mazzia, Francesca & Nagy, A.M., 2015. "A new mesh selection strategy with stiffness detection for explicit Runge–Kutta methods," Applied Mathematics and Computation, Elsevier, vol. 255(C), pages 125-134.
    • Handle: RePEc:eee:apmaco:v:255:y:2015:i:c:p:125-134
    DOI: 10.1016/j.amc.2014.03.065
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    Cited by:

    1. Amodio, P. & Iavernaro, F. & Mazzia, F. & Mukhametzhanov, M.S. & Sergeyev, Ya.D., 2017. "A generalized Taylor method of order three for the solution of initial value problems in standard and infinity floating-point arithmetic," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 141(C), pages 24-39.
    2. Ramos, Higinio & Rufai, M.A., 2018. "Third derivative modification of k-step block Falkner methods for the numerical solution of second order initial-value problems," Applied Mathematics and Computation, Elsevier, vol. 333(C), pages 231-245.

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