A new class of efficient general linear methods for ordinary differential equations

We describe the construction of a new class of efficient general linear methods of high stage order, for nonstiff and stiff differential systems. Examples of explicit methods with large regions of stability, and implicit methods which are A- and L-stable, up to the order p=4 are presented. It is con...

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Bibliographic Details
Published in:Applied numerical mathematics 2020-05, Vol.151, p.282-300
Main Authors: Braś, M., Jackiewicz, Z.
Format: Article
Language:English
Subjects:
Continuous extensions
General linear methods
Local discretization errors
Stability analysis
Stage order and order conditions
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Summary:We describe the construction of a new class of efficient general linear methods of high stage order, for nonstiff and stiff differential systems. Examples of explicit methods with large regions of stability, and implicit methods which are A- and L-stable, up to the order p=4 are presented. It is confirmed by numerical experiments that all methods achieve the expected order of accuracy and no order reduction occurs for stiff systems.
ISSN:0168-9274
1873-5460
DOI:10.1016/j.apnum.2019.12.022