Article ID Journal Published Year Pages File Type
4638993 Journal of Computational and Applied Mathematics 2014 13 Pages PDF
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 AA-, LL-, 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 ϵϵ-algebraic stability and investigate its consequences. Examples of ϵϵ-algebraically stable methods are given up to order p=4p=4.

Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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