Results 21 to 30 of about 822,876 (350)
A nonlocal physics-informed deep learning framework using the peridynamic differential operator [PDF]
arXiv.org, 2020 The Physics-Informed Neural Network (PINN) framework introduced recently incorporates physics into deep learning, and offers a promising avenue for the solution of partial differential equations (PDEs) as well as identification of the equation parameters.
E. Haghighat +3 more
semanticscholar +1 more source
Hyena neural operator for partial differential equations
APL Machine Learning, 2023 Numerically solving partial differential equations typically requires fine discretization to resolve necessary spatiotemporal scales, which can be computationally expensive. Recent advances in deep learning have provided a new approach to solving partial
Saurabh Patil +2 more
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Вестник КазНУ. Серия математика, механика, информатика, 2021 In this paper we consider the properties of the resolvent of a linear operator corresponding to a degenerate singular second-order differential equation with variable coefficients, considered in the Lebesgue space.
K. N. Ospanov, A. N. Yesbayev
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A new parametric differential operator generalized a class of d'Alembert's equations
Journal of Taibah University for Science, 2021 The studies in operator theory are attracting many researchers. The central aim of this investigation is to formulate a special parametric differential operator (PDO) based on the error function in the open unit disk. The suggested operator is related to
Ibtisam Aldawish, Rabha W. Ibrahim
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Stability of the fractional Volterra integro‐differential equation by means of ψ‐Hilfer operator [PDF]
Mathematical methods in the applied sciences, 2018 In this paper, using the Riemann‐Liouville fractional integral with respect to another function and the ψ−Hilfer fractional derivative, we propose a fractional Volterra integral equation and the fractional Volterra integro‐differential equation.
J. Sousa +2 more
semanticscholar +1 more source
Physics-Informed Deep Neural Operator Networks [PDF]
arXiv.org, 2022 Standard neural networks can approximate general nonlinear operators, represented either explicitly by a combination of mathematical operators, e.g., in an advection-diffusion-reaction partial differential equation, or simply as a black box, e.g., a ...
S. Goswami +3 more
semanticscholar +1 more source
Initial Problem for Two-Dimensional Hyperbolic Equation with a Nonlocal Term
Mathematics, 2022 In this paper, we study the Cauchy problem in a strip for a two-dimensional hyperbolic equation containing the sum of a differential operator and a shift operator acting on a spatial variable that varies over the real axis. An operating scheme is used to
Vladimir Vasilyev, Natalya Zaitseva
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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 \(k_0(x)\).
Olivier Cormier +3 more
openaire +2 more sources
On the “splitting” effect for multipoint differential operators with summable potential
Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2017 We study the differential operator of the fourth order with multipoint boundary conditions. The potential of the differential operator is summable function on a finite segment.
Sergey I Mitrokhin
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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
core +1 more source