On solving systems of autonomous ordinary differential equations by reduction to a variable of an algebra
type: Item
instance of: scholarly article
title: On solving systems of autonomous ordinary differential equations by reduction to a variable of an algebra
zbMATH Open document ID: 1254.34053
DOI: 10.1155/2012/753916
author: Alvaro Alvarez-Parrilla
author: Martín Eduardo Frías-Armenta
author: Elifalet López-González
author: Carlos Yee-Romero
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2012-10-16T00:00:00Z
review text: Summary: A new technique for solving a certain class of systems of autonomous ordinary differential equations over \(\mathbb K^n\) is introduced (\(\mathbb K\) being the real or complex field). The technique is based on two observations: (1) if \(\mathbb K^n\) has the structure of certain normed, associative, commutative algebras with a unit \(\mathbb A\) over \(\mathbb K\), then there is a scheme for reducing the system of differential equations to an autonomous ordinary differential equation on one variable of the algebra; (2) a technique, previously introduced for solving differential equations over \(\mathbb C\) is shown to work on the class mentioned in the previous paragraph. In particular, it is shown that the algebras in question include algebras linearly equivalent to the tensor product of matrix algebras of certain normal forms.
Mathematics Subject Classification ID: 34C20
Mathematics Subject Classification ID: 16-XX
zbMATH DE Number: 6093859
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/753916
OpenAlex ID: W2150631949
Wikidata QID: Q58705045
cites work: Q5820753
cites work: An outline of the theory of pseudoanalytic functions
cites work: Q5423507
cites work: Q5420825
cites work: On the relationship between \(p\)-analytic functions and Schrödinger equation
cites work: Q4672099
cites work: Associated spaces defined by ordinary differential equations
cites work: Q5708276
cites work: Q5452323
cites work: Q3281267
cites work: Mixed elastico-plasticity problems with partially unknown boundaries
cites work: Generalized analytic functions in 3d stokes flows
cites work: The Framework ofk-Harmonically Analytic Functions for Three-Dimensional Stokes Flow Problems, Part I
cites work: Q4716148
cites work: Dynamics Near the Essential Singularity of a Class of Entire Vector Fields
cites work: On Using Flows to Visualize Functions of a Complex Variable
cites work: Local and global phase portrait of equation \(\dot z=f(z)\)
cites work: Newton vector fields on the plane and on the torus
cites work: Julia Sets and Differential Equations
cites work: Q4856193
cites work: Newton's method and complex dynamical systems
cites work: A convergent process of price adjustment and global Newton methods
cites work: Q3995847
cites work: Q4029570
cites work: The Theory of Analytic Functions in Normed Abelian Vector Rings
cites work: From Generalized Cauchy-Riemann Equations to Linear Algebras
cites work: The generalized Laplace equations in a function theory for commutative algebras
cites work: Q3961610
cites work: Q5822548
cites work: Function theory of one complex variable.
cites work: Q4000467
description: scientific article; zbMATH DE number 6093859