Results 11 to 20 of about 243,415 (192)
Differential equations for algebraic functions [PDF]
Proceedings of the 2007 international symposium on Symbolic and algebraic computation, 2007 It is classical that univariate algebraic functions satisfy linear differential equations with polynomial coefficients. Linear recurrences follow for the coefficients of their power series expansions. We show that the linear differential equation of minimal order has coefficients whose degree is cubic in the degree of the function.
Bostan, Alin +4 more
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Solutions of algebraic differential equations
Journal of Differential Equations, 1983 This paper may be considered as a mathematical essay on the question “What is a solution of an algebraic differential equation?” Many theorems in differential algebra are proved by differentiating an algebraic differential equation several times, and then eliminating certain quantities, say, by the use of resultants.
Lee A. Rubel
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Algebraic and differential operator equations
Linear Algebra and its Applications, 1988 AbstractExplicit expressions for solutions of boundary-value problems and Cauchy problems related to the operator differential equation X(n)+An−1Xn−1)+⋯+A0X=0 are given in terms of solutions of the algebraic operator equation Xn+An−1Xn−1 +⋯+A0=0. A method for solving this algebraic equation is studied.
L. Jódar
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Singularities of algebraic differential equations [PDF]
Advances in Applied Mathematics, 2021 There exists a well established differential topological theory of singularities of ordinary differential equations. It has mainly studied scalar equations of low order. We propose an extension of the key concepts to arbitrary systems of ordinary or partial differential equations.
Lange-Hegermann, Markus +3 more
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Differential Algebraic Equations [PDF]
, 2021 AbstractLet H be a Hilbert space and $$\nu \in \mathbb {R}$$ ν ∈ ℝ . We saw in the previous chapter how initial value problems can be formulated within the framework of evolutionary equations.
Christian Seifert +2 more
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Differential Equivalence for Linear Differential Algebraic Equations [PDF]
IEEE Transactions on Automatic Control, 2022 Differential-algebraic equations (DAEs) are a widespread dynamical model that describes continuously evolving quantities defined with differential equations, subject to constraints expressed through algebraic relationships. As such, DAEs arise in many fields ranging from physics, chemistry, and engineering.
Stefano Tognazzi +3 more
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Transforming Radical Differential Equations to Algebraic Differential Equations
Mediterranean Journal of Mathematics, 2022 Abstract In this paper we present an algorithmic procedure that transforms, if possible, a given system of ordinary or partial differential equations with radical dependencies in the unknown function and its derivatives into a system with polynomial relations among them by means of a rational change of variables.
Falkensteiner, Sebastian, Sendra, Rafael
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Picard-Vessiot Extensions of Real Differential Fields [PDF]
, 2019 For a linear differential equation defined over a formally real differential field K with real closed field of constants k, Crespo, Hajto and van der Put proved that there exists a unique formally real Picard- Vessiot extension up to K-differential ...
Crespo, Teresa, Hajto, Zbigniew
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Algebraic Solutions of the Lam\'e Equation, Revisited [PDF]
, 2002 A minor error in the necessary conditions for the algebraic form of the Lam\'e equation to have a finite projective monodromy group, and hence for it to have only algebraic solutions, is pointed out. [See F. Baldassarri, "On algebraic solutions of Lam\'e'
Baldassarri +14 more
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Algebras and differential equations [PDF]
Nagoya Mathematical Journal, 1977 One purpose of this paper is a purely algebraic study of (systems of) ordinary differential equations of the typewhere the coefficients are taken from a fixed associative, commutative, unital ring R, such as the field R of real or C of complex numbers or a commutative, unital Banach algebra.
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