Construction of algebraically stable DIMSIMs

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:261

Article

Izzo, Giuseppe¹  Jackiewicz, Zdzislaw^2,3 

[1] Univ Naples Federico II, Dipartimento Matemat & Appl R Caccioppoli, I-80126 Naples, Italy

[2] Arizona State Univ, Dept Math, Tempe, AZ 85287 USA

[3] AGH Univ Sci & Technol, Krakow, Poland

关键词: General linear methods;    Order conditions;    Algebraic stability;   

DOI  :  10.1016/j.cam.2013.10.037

来源: Elsevier

【 摘 要 】

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 epsilon-algebraic stability and investigate its consequences. Examples of epsilon-algebraically stable methods are given up to order p = 4. (C) 2013 Elsevier B.V. All rights reserved.

【 授权许可】

Free