# Efficient General Linear Methods of High Order with Inherent Quadratic Stability

Michał Braś, Zdzislaw Jackiewicz

Research output: Contribution to journalArticle

1 Citation (Scopus)

### Abstract

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.

Original language English (US) 450-468 19 Mathematical Modelling and Analysis 19 4 https://doi.org/10.3846/13926292.2014.955893 Published - Jan 1 2014

### Fingerprint

General Linear Methods
Higher Order
Stability Condition
Roots
Internal

### Keywords

• A- and L-stability
• general linear methods
• order and stage order

### ASJC Scopus subject areas

• Analysis
• Modeling and Simulation

### Cite this

In: Mathematical Modelling and Analysis, Vol. 19, No. 4, 01.01.2014, p. 450-468.

Research output: Contribution to journalArticle

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