Formal and numerical processes of summation of series solutions of differential equations
type: Item
instance of: scholarly article
title: Formal and numerical processes of summation of series solutions of differential equations
zbMATH Open document ID: 0831.34003
author: Jean Thomann
published in: Expositiones Mathematicae
publication date: 1996-01-23T00:00:00Z
review text: The theories of \(k\)-summability (see [\textit{J. P. Ramis}, Lecture Notes in Physics 126, Springer (1980)]) and multisummability (see [\textit{J. Thomann}, Journées de printemps de la PRC Math-Info (1990)]) of formal power series solutions of differential equations lead to efficient computation methods. The author considers some aspects of the computation of the coefficients and of the sums of these series. He makes an essential use of computer algebra tools in order to control numerical processes.
Mathematics Subject Classification ID: 34M99
Mathematics Subject Classification ID: 30B10
Mathematics Subject Classification ID: 30B30
Mathematics Subject Classification ID: 30B40
Mathematics Subject Classification ID: 30E15
Mathematics Subject Classification ID: 34D05
Mathematics Subject Classification ID: 40A05
Mathematics Subject Classification ID: 65B10
Mathematics Subject Classification ID: 65L07
zbMATH DE Number: 797136
zbMATH Keywords: \(k\)-summability
zbMATH Keywords: multisummability
zbMATH Keywords: formal power series solutions
zbMATH Keywords: computer algebra
reviewed by: Hiroshi Haruki
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 797136