Results 21 to 30 of about 290,072 (190)
Analytical solution of fractional differential equations by Akbari–Ganji’s method
Partial Differential Equations in Applied Mathematics, 2022 According to the various and extensive applications of fractional calculus in a range of fields, such as engineering, biology, image processing, material science and economics, researchers have discovered new, simpler-to-use and more accurate approaches ...
M.A. Attar +3 more
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Journal of Optimization, Differential Equations and Their Applications, 2021 In this paper, we study the questions of the existence of global weak solutions and local strong solutions of paired stochastic functional differential equations in a Hilbert space, one of which is an equation with an unbounded operator, and the other is
Andrey O. Stanzhytskyi
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Polynomial solutions of differential–difference equations
Journal of Approximation Theory, 2011 We investigate the zeros of polynomial solutions to the differential-difference equation \[ P_{n+1}(x)=A_{n}(x)P_{n}^{\prime}(x)+B_{n}(x)P_{n}(x), n=0,1,... \] where $A_{n}$ and $B_{n}$ are polynomials of degree at most 2 and 1 respectively. We address the question of when the zeros are real and simple and whether the zeros of polynomials of adjacent ...
Dominici, Diego +2 more
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Invariants of kinetic differential equations
Electronic Journal of Qualitative Theory of Differential Equations, 2004 Polynomial differential equations showing chaotic behavior are investigated using polynomial invariants of the equations. This tool is more effective than the direct method for proving statements like the one: the Lorenz equation cannot be transformed ...
A. Halmschlager, L. Szenthe, J. Tóth
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Differential Galois Theory of Linear Difference Equations [PDF]
, 2008 We present a Galois theory of difference equations designed to measure the differential dependencies among solutions of linear difference equations.
Hardouin, Charlotte, Singer, Michael F.
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Linear Differential Operators for Polynomial Equations
Journal of Symbolic Computation, 2002 Let \(k_0\) be a number field and \(\overline{k_0}\) be its algebraic closure. Let \(P\in k_0(x)[y]\) be a squarefree polynomial in \(y\). The derivation \(\delta=\frac d{dx}\) extends uniquely to the algebraic closure \(\overline{k_0(x)}\) of \(k_0(x)\).
Cormier, Olivier +3 more
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Stability of delay differential equations via delayed matrix sine and cosine of polynomial degrees
Advances in Difference Equations, 2017 In this paper, we study the finite time stability of delay differential equations via a delayed matrix cosine and sine of polynomial degrees. Firstly, we give two alternative formulas of the solutions for a delay linear differential equation.
Chengbin Liang, Wei Wei, JinRong Wang
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Supersymmetric pairing of kinks for polynomial nonlinearities [PDF]
, 2004 We show how one can obtain kink solutions of ordinary differential equations with polynomial nonlinearities by an efficient factorization procedure directly related to the factorization of their nonlinear polynomial part.
E. Schrödinger +5 more
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Computing with polynomial ordinary differential equations
Journal of Complexity, 2016 In 1941, Claude Shannon introduced the General Purpose Analog Computer(GPAC) as a mathematical model of Differential Analysers, that is to say as a model of continuous-time analog (mechanical, and later one electronic) machines of that time. Following Shannon's arguments, functions generated by GPACs must be differentially algebraic.
Bournez, Olivier +2 more
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Powersum formula for polynomials whose distinct roots are differentially independent over constants
International Journal of Mathematics and Mathematical Sciences, 2002 We prove that the author's powersum formula yields a nonzero expression for a particular linear ordinary differential equation, called a resolvent, associated with a univariate polynomial whose coefficients lie in a differential field of characteristic ...
John Michael Nahay
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