General Nyström methods in Nordsieck form: error analysis

Raffaele D'Ambrosio ^[1] ; Giuseppe De Martino ^[1] ; Beatrice Paternoster ^[1]
1. [1] University of Salerno
  
  University of Salerno
  
  Fisciano, Italia
Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 292, Nº 1 (15 January 2016), 2016, págs. 694-702
Idioma: inglés
DOI: 10.1016/j.cam.2015.04.041
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Resumen
- 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.