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Computing Divisors and Common Multiples of Quasi-linear Ordinary Differential Equations
[chapter]

2013
*
Lecture Notes in Computer Science
*

We design an

doi:10.1007/978-3-319-02297-0_12
fatcat:72ipzs6ao5cy3g6hihw3jevvba
*algorithm*which finds first-order quasi-*linear*generalized divisors of*a*second-order quasi-*linear**ordinary**differential**equation*. ... We prove that*a*quasi-*linear*common multiple of*a*pair of quasi-*linear**equations*always exists and design an*algorithm*which yields*a*quasilinear common multiple. ... The first author is grateful to the Max-Planck Institut für Mathematik, Bonn*for*its hospitality during writing this paper and to Labex CEMPI (ANR-11-LABX-0007-01). ...##
###
Methods in Mathematica for Solving Ordinary Differential Equations
[article]

2011
*
arXiv
*
pre-print

An overview of the solution methods

arXiv:1104.4025v1
fatcat:2vgimuiaargp5lo54fihykkhwy
*for**ordinary**differential**equations*in the Mathematica function DSolve is presented. ... We hope that the examples and ideas outlined in this paper will be useful*for*elementary and advanced courses on*ordinary**differential**equations*, as well as*for*solving*differential**equations*which occur ... )*for*solving*differential**equations*. ...##
###
On linearization of third-order ordinary differential equations

2006
*
Journal of Physics A: Mathematical and General
*

*A*new

*algorithm*

*for*

*linearization*of

*a*third-order

*ordinary*

*differential*

*equation*is presented. ... The

*algorithm*consists of composition of two operations: reducing order of an

*ordinary*

*differential*

*equation*and using the Lie

*linearization*test

*for*the obtained second-order

*ordinary*

*differential*

*equation*... New

*algorithm*If the order of

*a*third-order

*ordinary*

*differential*

*equation*is reduced, then one can apply the Lie test

*for*

*linearization*. ...

##
###
Methods in Mathematica for Solving Ordinary Differential Equations

2011
*
Mathematical and Computational Applications
*

An overview of the solution methods

doi:10.3390/mca16040784
fatcat:ql7eirlz5beifbnsgian7a637e
*for**ordinary**differential**equations*in the Mathematica function DSolve is presented. ... We hope that the examples and ideas outlined in this paper will be useful*for*elementary and advanced courses on*ordinary**differential**equations*, as well as*for*solving*differential**equations*which occur ... )*for*solving*differential**equations*. ...##
###
Page 400 of Mathematical Reviews Vol. , Issue 91A
[page]

1991
*
Mathematical Reviews
*

*ordinary*

*differential*

*equations*. ... Some efficiently vectorizable

*algorithms*

*for*

*factorizing*these types of matrices and solving the corresponding

*linear*systems are described. ...

##
###
Symbolic Computation with Integro-Differential Operators

2016
*
Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation - ISSAC '16
*

*Differential*operators already provide

*a*rich algebraic structure with

*a*wealth of results and

*algorithmic*methods. ... In particular, we discuss normal forms, basic algebraic properties, and the computation of polynomial solutions

*for*

*ordinary*integro-

*differential*

*equations*with polynomial coefficients. ...

*For*studying

*linear*

*differential*

*equations*, the basic algebraic structure is the noncommutative ring of

*differential*operators over

*a*

*differential*algebra. ...

##
###
Computing Highest-Order Divisors for a Class of Quasi-Linear Partial Differential Equations
[chapter]

2015
*
Lecture Notes in Computer Science
*

We design an

doi:10.1007/978-3-319-24021-3_12
fatcat:t3cipzyyirgaxenq4pogckzu7i
*algorithm*which*for**a*class of quasi-*linear*partial*differential*polynomials of order k + 1 finds its quasi-*linear*divisors of order k. ...*A**differential*polynomial G is called*a*divisor of*a**differential*polynomial F if any solution of the*differential**equation*G = 0 is*a*solution of the*equation*F = 0. ... The first author is grateful to the Max-Planck Institut für Mathematik, Bonn*for*its hospitality during writing this paper and to Labex CEMPI (ANR-11-LABX-0007-01). ...##
###
Algebraic, rational and Puiseux series solutions of systems of autonomous algebraic ODEs of dimension one
[article]

2020
*
arXiv
*
pre-print

We establish

arXiv:2001.10992v1
fatcat:3ngrl76c2ffr5obhutxnzxprti
*a*relationship between the solutions of the system and the solutions of an associated first order autonomous*ordinary**differential**equation*, that we call the reduced*differential**equation*. ... Moreover, if the reduced*differential**equation*is non trivial,*for*every given point (x_0,y_0) in the complex plane, we prove the existence of*a*convergent Puiseux series solution y(x) of the original ... Note that in [4] it is shown that*for*general systems of algebraic*ordinary**differential**equations*the existence of non-constant formal power series solutions can not be decided*algorithmically*. ...##
###
Integrating linear ordinary fourth-order differential equations in the MAPLE programming environment

2021
*
Eastern-European Journal of Enterprise Technologies
*

This paper reports

doi:10.15587/1729-4061.2021.233944
fatcat:gpsftxmpavew3ivuaoldj6yqfu
*a*method to solve*ordinary*fourth-order*differential**equations*in the form of*ordinary*power series and,*for*the case of regular special points, in the form of generalized power series ... The program*for*solving*ordinary*fourth-order*differential**equations*could be used to construct Green's functions of boundary problems, to solve*differential**equations*with private derivatives,*a*system ... Study [12] presented two*algorithms**for*solving*ordinary**linear**differential**equations*of the second order. ...##
###
A Symbolic Framework for Operations on Linear Boundary Problems
[chapter]

2009
*
Lecture Notes in Computer Science
*

*For*

*ordinary*

*differential*

*equations*, the operations implemented include computing Green's operators, composing boundary problems and integrodifferential operators, and

*factoring*boundary problems. ... We describe

*a*symbolic framework

*for*treating

*linear*boundary problems with

*a*generic implementation in the Theorema system. ... We extended these results to

*a*

*differential*algebra setting in [4], where we also developed

*a*

*factorization*method applicable to boundary problems

*for*

*ordinary*

*differential*

*equations*(ODEs). ...

##
###
Page 4033 of Mathematical Reviews Vol. , Issue 89G
[page]

1989
*
Mathematical Reviews
*

*ordinary*

*differential*

*equations*by means of interval analytical methods. ... In this instructive paper the authors consider the initial value problem

*for*

*a*system of m

*ordinary*

*differential*

*equations*of first order with an interval input vector and

*a*perturbation parameter in the ...

##
###
Page 1243 of Mathematical Reviews Vol. , Issue 2001B
[page]

2001
*
Mathematical Reviews
*

The two

*algorithms**for*obtaining the orthogonal matrix Q at step k (in*factored*form) are formu- 65L*Ordinary**differential**equations*2001b:65075 lated and it is explained how to use them. ... The computation of the orthogonal*factor*Q of the QR factoriza- tion of some or all columns of the fundamental solution matrix Y of*a**linear*system of*ordinary**differential**equations*dY/dt =*A*(t)Y is considered ...##
###
Algebraic, Rational and Puiseux Series Solutions of Systems of Autonomous Algebraic ODEs of Dimension One

2020
*
Mathematics in Computer Science
*

We establish

doi:10.1007/s11786-020-00478-w
fatcat:6rvtd7orkrcijdnyhgira4qznu
*a*relationship between the solutions of the system and the solutions of an associated first order autonomous*ordinary**differential**equation*, that we call the reduced*differential**equation*. ... Moreover, if the reduced*differential**equation*is non trivial,*for*every given point (x 0 , y 0 ) ∈ C 2 , we prove the existence of*a*convergent Puiseux series solution y(x) of the original system such ... To view*a*copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. ...##
###
Page 1145 of Mathematical Reviews Vol. , Issue 84c
[page]

1984
*
Mathematical Reviews
*

Diestler, The discretization of continuous infinite sets of coupled

*ordinary**linear**differential**equations*: application to the collision-induced dissociation of*a*diatomic molecule by an atom (pp. 40-52 ... Ortiz, Approximation of eigenvalues defined by*ordinary**differential**equations*with the tau method (pp. 90-102); Axel Ruhe, The two-sided Arnoldi*algorithm**for*nonsymmetric eigenvalue problems (pp. 104 ...##
###
Computer Algebra Algorithms for Linear Ordinary Differential and Difference equations
[chapter]

2001
*
European Congress of Mathematics
*

Galois theory has now produced

doi:10.1007/978-3-0348-8266-8_9
fatcat:lrc2t5nvyvf25dbje33akytwai
*algorithms**for*solving*linear**ordinary**differential*and difference*equations*in closed form. ... After introducing the relevant parts of the theory, we describe the latest*algorithms**for*solving such*equations*. ... -*A*. Weil*for*their many useful comments and remarks during the preparation of this paper, as well as Prof. W. Decker*for*inviting me to present this survey at 3ecm. ...
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