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Frobenius Method for Computing Power Series Solutions of Linear Higher-Order Differential Systems
We consider the problem of computing regular formal solutions of systems of linear differential equations with analytic coefficients. The classical approach consists in reducing the system to anExpand
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Computing closed form solutions of integrable connections
TLDR
We present algorithms for computing rational and hyperexponential solutions of linear D-finite partial differential systems written as integrable connections by adapting existing algorithms handling ordinary linear differential systems. Expand
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On k-simple forms of first-order linear differential systems and their computation
TLDR
In this paper, we develop a direct method for computing a k-simple form (see Pflugel, 2000) of a singular linear differential system of first-order. Expand
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Méthodes algébriques pour la résolution d’équations différentielles matricielles d’ordre arbitraire
Dans cette these, nous developpons de nouvelles methodes algebriques pour la resolution d’une classe importante de systemes d’equations differentielles lineaires d’ordre arbitraire. De tels systemesExpand
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On simultaneous row and column reduction of higher-order linear differential systems
TLDR
We define simultaneously row and column reduced forms of higher-order linear differential systems with power series coefficients and give two algorithms, along with their complexities, for their computation. Expand
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Simple forms of higher-order linear differential systems and their applications in computing regular solutions
TLDR
We propose a direct algorithm for computing regular formal solutions of a given higher-order linear differential system near a singular point. Expand
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Simultaneously row- and column-reduced higher-order linear differential systems
TLDR
In this paper, we investigate the local analysis of systems of linear differential-algebraic equations (DAEs) and second-order linear differential systems and extend the formal reduction of first-order ODEs to higher-order systems. Expand
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Algorithms for regular solutions of higher-order linear differential systems
TLDR
We study systems of higher-order linear differential equations having a regular singularity at the origin. Expand
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A New Approach for Computing Regular Solutions of Linear Difference Systems
TLDR
In this paper, we provide a new approach for computing regular solutions of first-order linear difference systems. Expand
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Algebraic methods solving matrix differential equations of arbitrary order
Dans cette these, nous developpons de nouvelles methodes algebriques pour la resolution d’une classe importante de systemes d’equations differentielles lineaires d’ordre arbitraire. De tels systemesExpand
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