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

    Akram Movahedinejad Info
    Gholamreza Hojjati Info
    Ali Abdi Info
DOI: https://doi.org/10.3846/13926292.2017.1269024

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.

Keywords:

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

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January 11, 2017
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2017-01-11

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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

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