General Nystr枚m methods in Nordsieck form: Error analysis

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• 作者：Raffaele D&rsquo ; Ambrosio ^{rdambrosio@unisa.it" class="auth_mail" title="E-mail the corresponding author} ; Giuseppe De Martino ; ^{gdemartino@unisa.it" class="auth_mail" title="E-mail the corresponding author} ; Beatrice Paternoster ^{beapat@unisa.it" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Second order ordinary differential equations ; Multi-value numerical methods ; General Nyströ ; m methods ; Error analysis ; Order conditions
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2016
• 出版时间：15 January 2016
• 年：2016
• 卷：292
• 期：Complete
• 页码：694-702
• 全文大小：452 K

文摘

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.