Abstract
The class of general linear methods for ordinary differential equations combines the advantages of linear multistep methods (high efficiency) and Runge-Kutta methods (good stability properties such as A-, L-, or algebraic stability), while at the same time avoiding the disadvantages of these methods (poor stability of linear multistep methods, high cost for Runge-Kutta methods). In this paper we describe the construction of algebraically stable general linear methods based on the criteria proposed recently by Hewitt and Hill. We also introduce the new concept of ∈-algebraic stability and investigate its consequences. Examples of ∈-algebraically stable methods are given up to order p=4.
Original language | English (US) |
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Pages (from-to) | 72-84 |
Number of pages | 13 |
Journal | Journal of Computational and Applied Mathematics |
Volume | 261 |
DOIs | |
State | Published - 2014 |
Keywords
- Algebraic stability
- General linear methods
- Order conditions
ASJC Scopus subject areas
- Computational Mathematics
- Applied Mathematics