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A Universal Ordinary Differential Equation [PDF]
Logical Methods in Computer Science, 2020 An astonishing fact was established by Lee A. Rubel (1981): there exists a fixed non-trivial fourth-order polynomial differential algebraic equation (DAE) such that for any positive continuous function $\varphi$ on the reals, and for any positive ...
Olivier Bournez, Amaury Pouly
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Kernel Ordinary Differential Equations [PDF]
Journal of the American Statistical Association, 2020 Ordinary differential equation (ODE) is widely used in modeling biological and physical processes in science. In this article, we propose a new reproducing kernel-based approach for estimation and inference of ODE given noisy observations. We do not assume the functional forms in ODE to be known, or restrict them to be linear or additive, and we allow ...
Xiaowu Dai, Lexin Li
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On classical symmetries of ordinary differential equations related to stationary integrable partial differential equations [PDF]
Opuscula Mathematica, 2021 We study the relationship between the solutions of stationary integrable partial and ordinary differential equations and coefficients of the second-order ordinary differential equations invariant with respect to one-parameter Lie group.
Ivan Tsyfra
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Ordinary Differential Equations [PDF]
, 2021 AbstractIn this chapter, we discuss a first application of the time derivative operator constructed in the previous chapter. More precisely, we analyse well-posedness of ordinary differential equations and will at the same time provide a Hilbert space proof of the classical Picard–Lindelöf theorem (There are different notions for this theorem.
Christian Seifert +2 more
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Lie symmetry analysis of fractional ordinary differential equation with neutral delay
AIMS Mathematics, 2021 In this paper, Lie symmetry analysis method is employed to solve the fractional ordinary differential equation with neutral delay. The Lie symmetries for the fractional ordinary differential equation with neutral delay are obtained, and the group ...
Yuqiang Feng, Jicheng Yu
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Electronic Journal of Qualitative Theory of Differential Equations, 2022 In this paper, we present some uniqueness results for systems of ordinary differential equations. All of them are linked by a weak transversality condition at the initial condition, which generalizes those in the previous literature. Several examples are
José Ángel Cid +2 more
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Қарағанды университетінің хабаршысы. Математика сериясы, 2021 In the present paper the initial value problem for the second order ordinary differential equation with damping term and involution is investigated. We obtain equivalent initial value problem for the fourth order ordinary differential equations to the ...
A. Ashyralyev +2 more
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Mathematics, 2021 Discussions are presented by Morita and Sato in Mathematics 2017; 5, 62: 1–24, on the problem of obtaining the particular solution of an inhomogeneous ordinary differential equation with polynomial coefficients in terms of the Green’s function, in the ...
Tohru Morita, Ken-ichi Sato
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Mendel, 2022 This paper examines the implementation of simple combination mutation of differential evolution algorithm for solving stiff ordinary differential equations.
Werry Febrianti +2 more
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Gluon dynamics from an ordinary differential equation
European Physical Journal C: Particles and Fields, 2021 We present a novel method for computing the nonperturbative kinetic term of the gluon propagator from an ordinary differential equation, whose derivation hinges on the central hypothesis that the regular part of the three-gluon vertex and the ...
A. C. Aguilar +2 more
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