Numerical methods for ordinary differential equations with applications to partial differential equations [PDF]
, 1983 This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.The thesis develops a number of algorithms for the numerical solution of ordinary differential equations with applications to partial differential equations.
Khaliq, Abdul Qayyum Masud
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On linear systems and τ functions associated with Lamé's equation and Painlevé's equation VI. [PDF]
, 2011 Painleve's transcendental differential equation PVI may be expressed as the consistency condition for a pair of linear differential equations with 2 by 2 matrix coefficients with rational entries.
Gordon Blower, Blower, Gordon
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Explicit and implicit methods for second order ordinary differential equations [PDF]
, 1980 A family of explicit formulas is developed for solving a system of second order linear ordinary differential equations with constant coefficients and with initial conditions specified.
Twizell, E H
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Symbolic Analysis for Boundary Problems: From Rewriting to Parametrized Groebner Bases [PDF]
, 2010 We review our algebraic framework for linear boundary problems (concentrating on ordinary differential equations). Its starting point is an appropriate algebraization of the domain of functions, which we have named integro-differential algebras.
Regensburger, Georg +4 more
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Integrable operators and squares of Hankel operators. [PDF]
, 2008 Integrable operators arise in random matrix teory, where they describe the asymptotic distributions of large self-adjoint random matrices from the generalized unitary ensembles.
Blower, Gordon
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Pseudo-differential operators with symbols in modulation spaces
, 2010 We establish continuity results for pseudo-differential operators with symbols in modulation spaces, especially for spaces related to classical Wiener amalgam spaces.
Toft, Joachim,
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Reconstruction of Higher-Order Differential Operators by Their Spectral Data
Mathematics, 2022 This paper is concerned with inverse spectral problems for higher-order (n>2) ordinary differential operators. We develop an approach to the reconstruction from the spectral data for a wide range of differential operators with either regular or ...
Natalia P. Bondarenko
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Products of ordinary differential operators by evaluation and interpolation [PDF]
Proceedings of the twenty-first international symposium on Symbolic and algebraic computation, 2008 It is known that multiplication of linear differential operators over ground fields of characteristic zero can be reduced to a constant number of matrix products. We give a new algorithm by evaluation and interpolation which is faster than the previously-known one by a constant factor, and prove that in characteristic zero, multiplication of ...
Bostan, Alin +2 more
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Commuting Ordinary Differential Operators and the Dixmier Test [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2019 The Burchnall-Chaundy problem is classical in differential algebra, seeking to describe all commutative subalgebras of a ring of ordinary differential operators whose coefficients are functions in a given class. It received less attention when posed in the (first) Weyl algebra, namely for polynomial coefficients, while the classification of commutative
Previato, E., Rueda, S.L., Zurro, M.-A.
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Explicit Solutions of Singular Differential Equation by Means of Fractional Calculus Operators
Abstract and Applied Analysis, 2013 Recently, several authors demonstrated the usefulness of fractional calculus operators in the derivation of particular solutions of a considerably large number of linear ordinary and partial differential equations of the second and higher orders.
Resat Yilmazer, Okkes Ozturk
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