Construction of Nordsieck Second Derivative General Linear Methods with Inherent Quadratic Stability
DOI: https://doi.org/10.3846/13926292.2017.1269024Abstract
This paper describes the construction of second derivative general linear methods in Nordsieck form with stability properties determined by quadratic stability functions. This is achieved by imposing the so–called inherent quadratic stability conditions. After satisfying order and inherent quadratic stability conditions, the remaining free parameters are used to find the methods with L–stable property. Examples of methods with p = q = s = r − 1 up to order four are given.
Keywords:
stiff differential equations, second derivative methods, Nordsieck methods, inherent quadratic stability, A– and L–stabilityHow to Cite
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Copyright (c) 2017 The Author(s). Published by Vilnius Gediminas Technical University.
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Copyright (c) 2017 The Author(s). Published by Vilnius Gediminas Technical University.
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This work is licensed under a Creative Commons Attribution 4.0 International License.