AGH University of Science and Technology, Faculty of Applied Mathematics al. Mickiewicza 30, 30-059 Krakow, Poland; Jagiellonian University, Faculty of Mathematics and Computer Science ul. prof. S. Lojasiewicza 6, 30-348 Krakow, Poland
The present paper deals with the implementation in a variable-step algorithm of general linear methods in Nordsieck form with inherent quadratic stability and large stability regions constructed recently by Braś and Cardone. Various implementation issues such as rescale strategy, local error estimation, step-changing strategy and starting procedure are discussed. Some numerical experiments are reported, which show the performances of the methods and make comparisons with other existing methods.
Bras, M., Cardone, A., & D’Ambrosio, R. (2013). Implementation of explicit Nordsieck methods with inherent quadratic stability. Mathematical Modelling and Analysis, 18(2), 289-307. https://doi.org/10.3846/13926292.2013.785039
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