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Computability of Differential Equations [PDF]
, 2021 In this chapter, we provide a survey of results concerning the computability and computational complexity of differential equations. In particular, we study the conditions which ensure computability of the solution to an initial value problem for an ordinary differential equation (ODE) and analyze the computational complexity of a computable solution ...
Graça, Daniel, Zhong, Ning
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Linearized Asymptotic Stability for Fractional Differential Equations [PDF]
, 2016 We prove the theorem of linearized asymptotic stability for fractional differential equations. More precisely, we show that an equilibrium of a nonlinear Caputo fractional differential equation is asymptotically stable if its linearization at the ...
Cong, N. D. +3 more
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Linearisation of a second-order nonlinear ordinary differential equation
Acta Polytechnica, 2023 We analyse nonlinear second-order differential equations in terms of algebraic properties by reducing a nonlinear partial differential equation to a nonlinear second-order ordinary differential equation via the point symmetry f(v)∂v.
Adhir Maharaj +3 more
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A study on the bilinear equation of the sixth Painlevé transcendents [PDF]
arXiv, 2023 The sixth Painlev\'e equation is a basic equation among the non-linear differential equations with three fixed singularities, corresponding to Gauss's hypergeometric differential equation among the linear differential equations. It is known that 2nd order Fuchsian differential equations with three singular points are reduced to the hypergeometric ...
arxiv
Moment Boundedness of Linear Stochastic Delay Differential Equation with Distributed Delay [PDF]
, 2012 This paper studies the moment boundedness of solutions of linear stochastic delay differential equations with distributed delay. For a linear stochastic delay differential equation, the first moment stability is known to be identical to that of the ...
Lei, Jinzhi, Li, Xiong, Wang, Zhen
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On the Equivalence of Differential Equations in the Sense of Coincidence Reflecting Functions
Abstract and Applied Analysis, 2015 We use a new method for constructing some differential equations which are equivalent to a given equation in the sense of having the same reflecting function.
Zhengxin Zhou
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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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, 2009 System of semilinear ordinary differential equation and fractional differential equation of distributed order is investigated and solved in a mild and classical sense.
Atanackovic, Teodor M. +2 more
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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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Five-dimensional Monopole Equation with Hedge-Hog Ansatz and Abel's Differential Equation
, 2011 We review the generalized monopole in the five-dimensional Euclidean space. A numerical solution with the Hedge-Hog ansatz is studied. The Bogomol'nyi equation becomes a second order autonomous non-linear differential equation.
A. M. Polyakov +6 more
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