A class of explicit second derivative general linear methods for non-stiff ODEs

• Published in: Mathematical modelling and analysis Vol. 29; no. 4; pp. 621 - 640
• Main Authors: Sharifi, Mohammad, Abdi, Ali, Braś, Michal, Hojjati, Gholamreza
• Format: Journal Article
• Language: English
• Published: Vilnius Vilnius Gediminas Technical University 11.10.2024
• Subjects: Applied mathematics; general linear methods; non-stiff ODEs; order conditions; Ordinary differential equations; quadratic stability; second derivative methods; Stability; Iran; non-stiff ODEs; second derivative methods; quadratic stability; order conditions; general linear methods
• ISSN: 1392-6292; 1648-3510
• DOI: 10.3846/mma.2024.19325

In this paper, we construct explicit second derivative general linear methods (SGLMs) with quadratic stability and a large region of absolute stability for the numerical solution of non-stiff ODEs. The methods are constructed in two different cases: SGLMs with p = q = r = s and SGLMs with p = q and r = s = 2 in which p, q, r and s are respectively the order, stage order, the number of external stages and the number of internal stages. Examples of the methods up to order five are given. The efficiency of the constructed methods is illustrated by applying them to some well-known non-stiff problems and comparing the obtained results with those of general linear methods of the same order and stage order.