On combinatorial differential equations
type: Item
instance of: scholarly article
title: On combinatorial differential equations
zbMATH Open document ID: 0622.34013
DOI: 10.1016/0022-247X(86)90310-0
author: Gilbert Labelle
published in: Journal of Mathematical Analysis and Applications
publication date: 1986-01-01T00:00:00Z
review text: This article analyzes the solution set of a first order initial value differential problem of the form \(dy/dx=f(x,y)\), \(y(0)=0\) in the context of combinatorial species in the sense of A. Joyal. It turns out that many non-isomorphic combinatorial solutions are possible for a given problem, although they all have the same underlying generating series. The author gives many examples of this phenomenon and also elaborates a combinatorial Newton-Raphson iterative scheme for the construction of the solutions. The multidimensional case is treated explicitly.
reviewed by: N.L.Maria
Mathematics Subject Classification ID: 34A99
Mathematics Subject Classification ID: 65J99
zbMATH DE Number: 4008839
zbMATH Keywords: first order initial value differential problem
zbMATH Keywords: combinatorial species
zbMATH Keywords: non-isomorphic combinatorial solutions
zbMATH Keywords: Newton-Raphson iterative scheme
describes a project that uses: Cayley
describes a project that uses: MACSYMA
MaRDI profile type: Publication
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full work available at URL: 0022-247x(86)90310-0
OpenAlex ID: W2093914815
description: scientific article; zbMATH DE number 4008839