The problem of finding approximate solutions to nonlinear differential equations.
type: Item
instance of: scholarly article
title: The problem of finding approximate solutions to nonlinear differential equations.
zbMATH Open document ID: 1036.34008
author: A. M. Shloma
published in: Computational Mathematics and Mathematical Physics
publication date: 2003-07-01T00:00:00Z
review text: The author considers a system of ordinary differential equations of the form \[ \dot x=A(x),\qquad x(t_0)=x_0,\tag{1} \] where \(A\) is a known nonlinear operator, \(A:{\mathbb R}^n\longrightarrow{\mathbb R}^n, x\in{\mathbb R}^n, t\in{\mathbb R}^1\), and \(x(t_0)=x_0\) are the initial conditions. He is looking for a solution to (1) in a range of initial values and, next, which is continued to a wider domain by using a pseudo-Taylor factorization of the nonlinear operator \(A(x)\).
Mathematics Subject Classification ID: 34A45
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 65L05
zbMATH DE Number: 1940686
zbMATH Keywords: ordinary differential equations
zbMATH Keywords: nonlinear operator
zbMATH Keywords: factorization
zbMATH Keywords: numerical-analytical solution
reviewed by: A. Tret'yakov
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1940686