General Nyström methods in Nordsieck form: Error analysis

The paper is concerned with the analysis of the error associated to a family of multi-value numerical methods for the solution of initial value problems based on special second order ordinary differential equations. Such methods, denoted as General Nyström methods, provide at each step point an appr...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2016-01, Vol.292, p.694-702
Main Authors: D’Ambrosio, Raffaele, De Martino, Giuseppe, Paternoster, Beatrice
Format: Article
Language:English
Subjects:
Approximation
Differential equations
Error analysis
General Nyström methods
Initial value problems
Mathematical analysis
Mathematical models
Multi-value numerical methods
Order conditions
Second order ordinary differential equations
Truncation errors
Vectors (mathematics)
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Summary:The paper is concerned with the analysis of the error associated to a family of multi-value numerical methods for the solution of initial value problems based on special second order ordinary differential equations. Such methods, denoted as General Nyström methods, provide at each step point an approximation to the Nordsieck vector associated to the solution of the problem. Order issues for such methods based on the theory of rooted trees are here provided, as well as an accuracy analysis is carried out, leading to a representation of the local truncation error.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2015.04.041