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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.
Bostan, Alin +4 more
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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.
Markus Lange-Hegermann +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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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 +1 more
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Differential-Algebraic Equations [PDF]
, 2006 Workshop ...
Peter Kunkel, Volker Mehrmann
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LIE ALGEBRAIC DISCRETIZATION OF DIFFERENTIAL EQUATIONS [PDF]
Modern Physics Letters A, 1995 A certain representation for the Heisenberg algebra in finite difference operators is established. The Lie algebraic procedure of discretization of differential equations with isospectral property is proposed. Using sl 2-algebra based approach, (quasi)-exactly-solvable finite difference equations are described.
Smirnov, Yuri, Turbiner, Alexander
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Green's Matrix for a Second Order Self-Adjoint Matrix Differential Operator [PDF]
, 2009 A systematic construction of the Green's matrix for a second order, self-adjoint matrix differential operator from the linearly independent solutions of the corresponding homogeneous differential equation set is carried out.
Bayram Tekin +12 more
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Rainich theory for type D aligned Einstein-Maxwell solutions [PDF]
, 2007 The original Rainich theory for the non-null Einstein-Maxwell solutions consists of a set of algebraic conditions and the Rainich (differential) equation.
B. Coll +21 more
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Nonlinear Eigenvalue Approach to Differential Riccati Equations for Contraction Analysis [PDF]
, 2016 In this paper, we extend the eigenvalue method of the algebraic Riccati equation to the differential Riccati equation (DRE) in contraction analysis. One of the main results is showing that solutions to the DRE can be expressed as functions of nonlinear ...
Kawano, Yu, Ohtsuka, Toshiyuki
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Generic planar algebraic vector fields are disintegrated
, 2020 In this article, we study model-theoretic properties of algebraic differential equations of order $2$, defined over constant differential fields. In particular, we show that the set of solutions of a general differential equation of order $2$ and of ...
Jaoui, Rémi
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