Results 11 to 20 of about 353 (182)

An Analysis of the Theta-Method for Pantograph-Type Delay Differential Equations

Complexity, 2022
The pantograph equation arises in electrodynamics as a delay differential equation (DDE). In this article, we provide the ϑ-method for numerical solutions of pantograph equations. We investigate the stability conditions for the numerical schemes.
Fathalla A. Rihan, Ahmed F. Rihan
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Nonlinear Pantograph-Type Diffusion PDEs: Exact Solutions and the Principle of Analogy

Mathematics, 2021
We study nonlinear pantograph-type reaction–diffusion PDEs, which, in addition to the unknown u=u(x,t), also contain the same functions with dilated or contracted arguments of the form w=u(px,t), w=u(x,qt), and w=u(px,qt), where p and q are the free ...
Andrei D. Polyanin, Vsevolod G. Sorokin
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A study of Hilfer-Katugampola type pantograph equations with complex order

Examples and Counterexamples, 2022
This article deals with existence, uniqueness and Ulam–Hyers–Rassias stability solutions for complex order Hilfer-Katugampola type pantograph equations involving initial and nonlocal condition.
S. Harikrishnan, E.M. Elsayed, K. Kanagarajan, D. Vivek   +3 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, Koroma, Mohammed Abdulai   +1 more
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A New Result for ψ-Hilfer Fractional Pantograph-Type Langevin Equation and Inclusions

Journal of Mathematics, 2022
In this paper, we deal with the existence and uniqueness of solution for ψ-Hilfer Langevin fractional pantograph differential equation and inclusion; these types of pantograph equations are a special class of delay differential equations.
Hamid Lmou, Khalid Hilal, Ahmed Kajouni
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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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Operational matrix based on Genocchi polynomials for solution of delay differential equations

Ain Shams Engineering Journal, 2018
In this paper, we present a new simple and effective algorithm for solving generalized Pantograph equations, delay differential equations with neutral terms and delay differential system with constant and variable coefficients.The new method is based on ...
Abdulnasir Isah, Chang Phang
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Almost Sure Exponential Stability of Numerical Solutions for Stochastic Pantograph Differential Equations with Poisson Jumps

Mathematics, 2022
The stability analysis of the numerical solutions of stochastic models has gained great interest, but there is not much research about the stability of stochastic pantograph differential equations.
Amr Abou-Senna, Boping Tian
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