Results 11 to 20 of about 353 (183)
Advances in Difference Equations, 2020 This study investigates the solutions of an impulsive fractional differential equation incorporated with a pantograph. This work extends and improves some results of the impulsive fractional differential equation.
Idris Ahmed +4 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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Approximation Algorithm for a System of Pantograph Equations [PDF]
Journal of Applied Mathematics, 2012 We show how to adapt an efficient numerical algorithm to obtain an approximate solution of a system of pantograph equations. This algorithm is based on a combination of Laplace transform and Adomian decomposition method. Numerical examples reveal that the method is quite accurate and efficient, it approximates the solution to a very high degree of ...
Widatalla, Sabir +1 more
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Advances in Mechanical Engineering, 2023 During the operation of high-speed railway, the transition-point disappearance phenomenon, which is caused by the deformation of pantograph head, poses a safety threat to the pantograph-catenary system.
Junqing Chen +5 more
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Stability analysis of pantograph under frictional force
Nihon Kikai Gakkai ronbunshu, 2019 The frictional force acts to the travelling pantograph head in horizontal direction due to sliding of the pantograph head and contact wire. Therefore, vertical motion of the pantograph head is generated by link mechanism of the pantograph.
Shigeyuki KOBAYASHI +2 more
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Energies, 2020 The pantograph catenary system plays an important role in the power performance of electric mining vehicles. A pantograph catenary system combining both a pantograph and a catenary is one of the most promising solutions.
Yinping Li, Tianxu Jin, Li Liu, Kun Yuan
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On Pantograph Integro-Differential Equations
Journal of Integral Equations and Applications, 1994 The authors study the initial value problem for pantograph integro- differential equations of the form \[ y'(t) = a y(t) + \int^ 1_ 0 y(qt) d \mu (q) + \int^ 1_ 0 y'(qt) d \nu (q),\;t > 0, \quad y(0) = y_ 0, \tag{1} \] where \(a\) is a complex constant, \(\mu (q)\) and \(\nu (q)\) are complex-valued functions of bounded variation on \([0,1]\). Denote \(
Iserles, Arieh, Liu, Yunkang
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The stability analysis of a discretized pantograph equation [PDF]
Mathematica Bohemica, 2011 Summary: The paper deals with a difference equation arising from the scalar pantograph equation via the backward Euler discretization. A case when the solution tends to zero but after reaching a certain index it loses this tendency is discussed. We analyse this problem and estimate the value of such an index.
Jánský, J., Kundrát, Petr
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IEEE Access, 2021 The aim of this study is to design a layer structure of feed-forward artificial neural networks using the Morlet wavelet activation function for solving a class of pantograph differential Lane-Emden models. The Lane-Emden pantograph differential equation
Kashif Nisar +7 more
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Boundary Value Problems, 2023 In this present manuscript, by applying fractional quantum calculus, we study a nonlinear fractional pantograph q-difference equation with nonlocal boundary conditions.
Adel Lachouri +2 more
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