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Construction of Nordsieck Second Derivative General Linear Methods with Inherent Quadratic Stability

    Akram Movahedinejad Affiliation
    ; Gholamreza Hojjati Affiliation
    ; Ali Abdi Affiliation

Abstract

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.

Keyword : stiff differential equations, second derivative methods, Nordsieck methods, inherent quadratic stability, A– and L–stability

How to Cite
Movahedinejad, A., Hojjati, G., & Abdi, A. (2017). Construction of Nordsieck Second Derivative General Linear Methods with Inherent Quadratic Stability. Mathematical Modelling and Analysis, 22(1), 60-77. https://doi.org/10.3846/13926292.2017.1269024
Published in Issue
Jan 11, 2017
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This work is licensed under a Creative Commons Attribution 4.0 International License.