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CONVODE: a reduce package for solving differential equations
1993
Journal of Computational and Applied Mathematics
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The package CONVODE (CONVersion of Ordinary Differential Equations) is written in order to study differential equations and systems of differential equations. ...
., CONVODE: a REDUCE package for solving differential equations, Journal of Computational and Applied Mathematics 48 (1993) 157-165. ...
It is evident that the parameter y1 associated to the degree of the polynomial, which is in the differential equation, must have a numerically fixed entire value. ...
doi:10.1016/0377-0427(93)90320-b
fatcat:wlsxwrskxzh2hnpbhjqvnd5kay
Page 7905 of Mathematical Reviews Vol. , Issue 2002K
[page]
2002
Mathematical Reviews
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The author, in the case d = 2, answers this question in the negative by producing a family of homogeneous vector fields SLV;, depending on a parameter / € N, such that SLV, has no homogeneous rational ...
Summary: “In this paper, we discuss the polynomial solutions of algebraic differential equations. ...
Oscillation of Linear Ordinary Differential Equations: On a Theorem of A. Grigoriev
2006
Journal of dynamical and control systems
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2004 pre-print arXiv:math/0409198v1 fatcat:bwbyu4rlb5fgrnqmrnpmo47xau
Grigoriev, placing an upper bound for the number of roots of linear combinations of solutions to systems of linear equations with polynomial or rational coefficients. ...
We give a simplified proof and an improvement of a recent theorem by A. ...
Any linear combination of solutions of the system (4.1) satisfies a linear nth order differential equation of the form (1.1) with polynomial coefficients a j ∈ C[t], polynomially depending on the parameters ...
doi:10.1007/s10450-006-0008-8
fatcat:oi24crrokresharppp46kitv4m
Polynomial solutions of N th order non-homogeneous differential equations
2002
International Journal of Mathematical Education in Science and Technology
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It was shown in 1 that the homogeneous differential equation has a finite polynomial solution if and only if where n is a root of the recurrence relation. ...
In this paper, the case in which the equation has a forcing term on the right hand side is considered. ...
From the general theory of linear differential equations, it is known that the general solution of 9 is: y Px i0 N c i y i x where y i x are n linearly independent homogenous solutions. ...
doi:10.1080/002073902321093577
fatcat:e5ielxwjrzbc5fd32tjwiwf3ba
On Ordinary, Linear q-Difference Equations, with Applications to q-Sato Theory
2015
Journal of Operators
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The purpose of this paper is to develop the theory of ordinary, linear q-difference equations, in particular the homogeneous case; we show that there are many similarities to differential equations. ...
In the second part we study the applications to a q-analogue of Sato theory. The q-Schur polynomials act as basis function, similar to q-Appell polynomials. ...
We assume that since the equation is of order , its general solution will depend on distinct arbitrary constants and proceed to consider the mode of this dependence. ...
doi:10.1155/2015/824549
fatcat:yctotvnbfna5fdmsi5nrhdb23i
Mellin–Barnes representations of Feynman diagrams, linear systems of differential equations, and polynomial solutions
2012
Physics Letters B
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We argue that the Mellin-Barnes representations of Feynman diagrams can be used for obtaining linear systems of homogeneous differential equations for the original Feynman diagrams with arbitrary powers ...
These systems of differential equations can be used (i) for the differential reductions to sets of basic functions and (ii) for counting the numbers of master integrals. ...
Any polynomial (rational) solution of a multivariable linear system of differential equations related to a Feynman diagram can be written as a product of one-loop bubble integrals and massless propagator ...
doi:10.1016/j.physletb.2012.06.045
fatcat:56kqwfgp3batpezhsm6eqokf74
Formal solutions of differential equations
1990
Journal of symbolic computation
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P o w e r Series Solutions of Differential E q u a t i o n s My aim here is to contrast what is known about linear differential equations with what is known about non-linear differential equations. ...
Good general references for information about linear differential equations are Poole (1960) and Schlesinger (1895). ...
So far, we have only been considering homogeneous linear differential equations, but one can ask the same questions about non-homogeneous linear differential equations L(y) = b. ...
doi:10.1016/s0747-7171(08)80037-5
fatcat:rz54tv4j3jezxjxugn22mr4kji
Page 210 of Mathematical Reviews Vol. , Issue 90A
[page]
1990
Mathematical Reviews
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The author gives theorems about the form of particular solutions of fourth-order nonhomogeneous and homogeneous ordinary differ- ential equations of Fuchs type, as an application of the fractional calculus ...
The constant N depends on A(t), r and é. L. J. ...
Page 75 of Mathematical Reviews Vol. 28, Issue 1
[page]
1964
Mathematical Reviews
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depending on z € Q
and ¢ €[0, co). ...
Under suitable restrictions on the functions C,(¢) and the coefficients of A, he proved that any solution of (1), sub- ject to certain homogeneous boundary conditions, that
75 ...
Analytical solutions to second order differential equations
1977
Computers and Mathematics with Applications
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A computer program, DIFFER, is described that will find analytical solutions to certain-second order ordinary differential equations. ...
An interactive main program is included which calls DIFFER and which will enable the user to run the program from a terminal. ...
Depending on which of the 4 expressions occur, the form of the particular solution is chosen and substituted into the differential equation yielding a set of simultaneous linear equations in which to solve ...
doi:10.1016/0898-1221(77)90110-9
fatcat:3qs4uwqp7bcdnlgnrpwcnaiyfu
Algorithms and methods in differential algebra
1996
Theoretical Computer Science
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In this talk, I do not intend to give an exhaustive survey of algorithmic aspects of Differential Algebra but I only propose some ReSum4 L'algGbre diffirentielle a Ctt fond&e par J.F. ...
Ritt, Differential Algebra is a true part of Algebra so that constructive and algorithmic problems and methods appear in this field. ...
Acknowledgements It is a great pleasure for me to thank Jean-Marie Strelcyn for very helpful discussions on first integrals and especially for having drawn my attention to genericity results in this domain ...
doi:10.1016/0304-3975(95)00179-4
fatcat:qdnoqabglzbkxj4uz64udyff5y
Integrability of Stochastic Birth-Death processes via Differential Galois Theory
[article]
2019
arXiv
pre-print
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A system of infinite, coupled ordinary differential equations (the so-called master equation) describes the time-dependence of the probability of each system state. ...
In this contribution we analyze the integrability of two types of stochastic birth-death processes (with polynomial birth and death rates) using standard differential Galois theory. ...
Acknowledgements The authors kindly thank to the members of our Integrability Madrid Seminar for many fruitful discussions: Rafael Hernández-Heredero, Sonia Jiménez-Verdugo, Alvaro Pérez-Raposo, José Rojo-Montijano ...
arXiv:1901.06266v1
fatcat:wu5l7fazczcpbk2vwtjuo44v5y
Multiparameter spectral theory
1968
Bulletin of the American Mathematical Society
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In one of these we allow nonlinear dependence on the scalar parameter, in particular, polynomial or rational dependence. In the matrix context, this is the topic of X-matrices (see e.g. [67] ). ...
However, the exploitation of this area in the spirit of classical analysis, in particular for ordinary differential equations, has reached no more than a preliminary stage. ...
In one of these we allow nonlinear dependence on the scalar parameter, in particular, polynomial or rational dependence. In the matrix context, this is the topic of X-matrices (see e.g. [67] ). ...
doi:10.1090/s0002-9904-1968-11866-x
fatcat:jhnckmf4pzdofoqieis2edrec4
Painlevé versus Fuchs
2006
Journal of Physics A: Mathematical and General
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2006 pre-print arXiv:math-ph/0602010v2 fatcat:4nqq6yx6pzgezdg4ui736sd5fyOther Versions
However, when there are certain restrictions on the four parameters there exist one parameter families of solutions which do satisfy (Fuchsian) differential equations of finite order. ...
The sigma form of the Painlevé VI equation contains four arbitrary parameters and generically the solutions can be said to be genuinely "nonlinear" because they do not satisfy linear differential equations ...
One can then deduce that the parameter u is a solution of a Riccati differential equation. ...
doi:10.1088/0305-4470/39/39/s16
fatcat:wpbecjserfaw5nvu7s4chjdm3i
On Hamiltonian potentials with quartic polynomial normal variational equations
[article]
2012
arXiv
pre-print
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In this paper we prove that there exists only one family of classical Hamiltonian systems of two degrees of freedom with invariant plane Γ={q_2=p_2=0} whose normal variational equation around integral ...
curves in Γ is generically a Hill-Schrödinger equation with quartic polynomial potential. ...
Acknowledgements The research of the first author is partially supported by grant FPI Spanish Government, project BFM2003-09504-C02-02. ...
arXiv:0809.0135v2
fatcat:wz5vyo4nefgsfcl7flp6h25z2e
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