Results 31 to 40 of about 370 (174)
A new numerical method to solve pantograph delay differential equations with convergence analysis
Advances in Difference Equations, 2021 The main aim presented in this article is to provide an efficient transferred Legendre pseudospectral method for solving pantograph delay differential equations.
H. Jafari +2 more
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Applied Sciences, 2021 In this paper, the authors present a mathematical and engineering model to optimally calculate the dynamic equation on the pantograph–catenary interaction when considering a rigid catenary with an overlapping span.
Jesús Benet +4 more
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On Bounded Solutions of the Balanced Generalized Pantograph Equation [PDF]
, 2008 The question about the existence and characterization of bounded solutions to linear functional-differential equations with both advanced and delayed arguments was posed in early 1970s by T. Kato in connection with the analysis of the pantograph equation, y'(x)=ay(qx)+by(x).
Bogachev, Leonid +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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A Study of Generalized Hybrid Discrete Pantograph Equation via Hilfer Fractional Operator
Fractal and Fractional, 2022 Pantograph, a device in which an electric current is collected from overhead contact wires, is introduced to increase the speed of trains or trams. The work aims to study the stability properties of the nonlinear fractional order generalized pantograph ...
Wafa Shammakh +3 more
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IEEE Access, 2019 In high-speed railways, the quality of current collection of high-speed train is directly determined by the contact force between the contact wire of the catenary and the registration strip of the pantograph.
Jing Zhang +4 more
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Shock and Vibration, 2014 In high-speed electric trains, a pantograph is mounted on the roof of the train to collect power through contact with an overhead catenary wire. The effect of fast harmonic and parametric excitation on a stochastically driven pantograph-catenary system ...
R. H. Huan, W. Q. Zhu, F. Ma, Z. H. Liu
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Journal of Function Spaces, 2022 The main goal of this paper is to develop a new formula of the fractional derivatives of the shifted Chebyshev polynomials of the third kind. This new formula expresses approximately the fractional derivatives of these polynomials in the Caputo sense in ...
Y. H. Youssri +2 more
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Computer simulation of pantograph delay differential equations
Thermal Science, 2021 Ritz method is widely used in variational theory to search for an approximate solution. This paper suggests a Ritz-like method for integral equations with an emphasis of pantograph delay equations. The unknown parameters involved in the trial solution can be determined by balancing the fundamental terms.
Xian-Yong Liu, Yan-Ping Liu, Zeng-Wen Wu
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The stability of modified Runge-Kutta methods for the pantograph equation [PDF]
Mathematics of Computation, 2006 In the present paper, the modified Runge-Kutta method is constructed, and it is proved that the modified Runge-Kutta method preserves the order of accuracy of the original one. The necessary and sufficient conditions under which the modified Runge-Kutta methods with the variable mesh are asymptotically stable are given. As a result,
M. Z. Liu, Z. W. Yang, Y. Xu
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