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
Authors who publish with this journal agree to the following terms
that this article contains no violation of any existing copyright or other third party right or any material of a libelous, confidential, or otherwise unlawful nature, and that I will indemnify and keep indemnified the Editor and THE PUBLISHER against all claims and expenses (including legal costs and expenses) arising from any breach of this warranty and the other warranties on my behalf in this agreement;
that I have obtained permission for and acknowledged the source of any illustrations, diagrams or other material included in the article of which I am not the copyright owner.
on behalf of any co-authors, I agree to this work being published in the above named journal, Open Access, and licenced under a Creative Commons Licence, 4.0 https://creativecommons.org/licenses/by/4.0/legalcode. This licence allows for the fullest distribution and re-use of the work for the benefit of scholarly information.
For authors that are not copyright owners in the work (for example government employees), please contact VILNIUS TECHto make alternative agreements.
