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 ϵ-algebraic stability and investigate its consequences. Examples of ϵ-algebraically stable methods are given up to order p=4.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
