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Efficient General Linear Methods of High Order with Inherent Quadratic Stability

    Michal Bras Affiliation
    ; Zdzislaw Jackiewicz Affiliation

Abstract

We search for general linear methods with s internal stages and r = s + 1 external stages of order p = s + 1 and stage order q = s. We require that stability function of these methods has only two non-zero roots. This is achieved by imposing the so-called inherent quadratic stability conditions. Examples of such general linear methods which are A- and L-stable up to the order p = 8 and stage order q = p - 1 are derived.

Keyword : general linear methods, order and stage order, A- and L-stability, inherent quadratic stability

How to Cite
Bras, M., & Jackiewicz, Z. (2014). Efficient General Linear Methods of High Order with Inherent Quadratic Stability. Mathematical Modelling and Analysis, 19(4), 450-468. https://doi.org/10.3846/13926292.2014.955893
Published in Issue
Sep 1, 2014
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This work is licensed under a Creative Commons Attribution 4.0 International License.