Cell Division And The Pantograph Equation [PDF]
ESAIM: Proceedings and Surveys, 2018 Simple models for size structured cell populations undergoing growth and division produce a class of functional ordinary differential equations, called pantograph equations, that describe the long time asymptotics of the cell number density.
van Brunt B., Zaidi A. A., Lynch T.
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Machine Learning for Modeling the Singular Multi-Pantograph Equations. [PDF]
Entropy (Basel), 2020 In this study, a new approach to basis of intelligent systems and machine learning algorithms is introduced for solving singular multi-pantograph differential equations (SMDEs). For the first time, a type-2 fuzzy logic based approach is formulated to find an approximated solution.
Mosavi A +5 more
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Quasirandom Graphs and the Pantograph Equation. [PDF]
Am Math Mon, 2021 To appear in Amer.
Shapira A, Tyomkyn M.
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Stochastic θ-Methods for a Class of Jump-Diffusion Stochastic Pantograph Equations with Random Magnitude [PDF]
The Scientific World Journal, 2014 This paper is concerned with the convergence of stochastic θ-methods for stochastic pantograph equations with Poisson-driven jumps of random magnitude.
Hua Yang, Feng Jiang
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Spectral-Collocation Methods for Fractional Pantograph Delay-Integrodifferential Equations [PDF]
Advances in Mathematical Physics, 2013 We propose and analyze a spectral Jacobi-collocation approximation for fractional order integrodifferential equations of Volterra type with pantograph delay. The fractional derivative is described in the Caputo sense. We provide a rigorous error analysis
Yin Yang, Yunqing Huang
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Accurate Solution for the Pantograph Delay Differential Equation via Laplace Transform
Mathematics, 2023 The Pantograph equation is a fundamental mathematical model in the field of delay differential equations. A special case of the Pantograph equation is well known as the Ambartsumian delay equation which has a particular application in Astrophysics.
Reem Alrebdi, Hind K. Al-Jeaid
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Lyapunov Stability of the Generalized Stochastic Pantograph Equation [PDF]
Journal of Mathematics, 2018 The purpose of the paper is to study stability properties of the generalized stochastic pantograph equation, the main feature of which is the presence of unbounded delay functions. This makes the stability analysis rather different from the classical one.
Ramazan Kadiev, Arcady Ponosov
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The establishment and validation of pantograph and overhead conductor rail dynamic simulation
Energy Reports, 2022 Overhead conductor rail which has become the main form of the overhead catenary, is widely used in China’s urban rail transit. In order to understand the vibration behavior of pantograph and conductor rail, it is necessary to carry out the study of the ...
Jinfa Guan +3 more
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Stability of the Discretized Pantograph Differential Equation [PDF]
Mathematics of Computation, 1993 In this paper we study discretizations of the general pantograph equation \[ y ′ ( t ) = a y ( t ) + b y ( θ ( t ) ) + c y ′ ( ϕ ( t )
Buhmann, Martin, Iserles, Arieh
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Analysis of stochastic pantograph differential equations with generalized derivative of arbitrary order [PDF]
E-Journal of Analysis and Applied Mathematics, 2022 In this paper, we mainly study the existence of analytical solutions of stochastic pantograph differential equations. The standard Picard’s iteration method is used to obtain the theory.
Devaraj Vivek +2 more
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