-Approximate polynomial solutions for the multi-pantograph equation with variable coefficients

Bota, Constantin; Căruntu, Bogdan

doi:10.1016/j.amc.2012.08.017

Cited by 6 publications

(2 citation statements)

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“…In recent years, many specific cases of the model problem considered in this work are encountered in the literature [5,7,10,11,12,13,20,23,26,28]. Our approach can be implemented for these specific problems quite easily.…”

Section: Introductionmentioning

confidence: 98%

A novel approach to construct the adjoint problem for a first-order functional integro-differential equation with general nonlocal condition

Özen

Oruçoğlu

2014

Lith Math J

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In this work, with the aim of determining Green's solution or generalized Green's solution, we propose a novel constructive approach by which a linear or specific nonlinear problem involving general linear nonlocal condition for a first-order functional ordinary integro-differential equation with general nonsmooth coefficients satisfying some general properties such as p-integrability and boundedness is reduced to an integral equation. A system of two integro-algebraic equations, called "the adjoint system," is constructed for this problem. Green's functional for the problem with trivial kernel and generalized Green's functional for the problem with nontrivial kernel are the unique solutions to the specific cases of this adjoint system. Green's functional and generalized Green's functional have two components. Their first components correspond to Green's function and generalized Green's function for the problem, respectively. Some illustrative applications are provided with known and unknown results.MSC: 34B10, 34B27, 34K10, 34K30, 45J05, 47A05

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Section: Introductionmentioning

confidence: 98%

A novel approach to construct the adjoint problem for a first-order functional integro-differential equation with general nonlocal condition

Özen

Oruçoğlu

2014

Lith Math J

View full text Add to dashboard Buy / Rent full text

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“…The pantograph equations are one of the important classes of delay differential equations, which arise in many scientific models such as population studies, controls of mechanical systems, medical biology, electrodynamics and dynamical systems etc., and they also arise in modeling of various phenomena in science and engineering [1,2,3]. These equations have been investigated by many authors and both analytical and numerical methods have been developed, some of which are Runge-Kutta and modified Runge-Kutta methods [4,5], differential transform method [6], Taylor collocation method [7], variational iteration method [8,9], homotopy perturbation method [10], ε-Approximate polynomial method [11], shifted Chebyshev polynomial approximation [12] and various collocation methods [13,14,15,16,17,18,19].…”

Section: Introductionmentioning

confidence: 99%

A new collocation method based on Euler polynomials for solution of generalized pantograph equations

Bayram¹,

Ibis²

2016

ntmsci

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In this paper, a new collocation method based on Euler polynomials is improved for the numerical solution of generalized pantograph equations. This method transforms the generalized pantograph equations into the matrix equation with the help of Euler polynomials and collocation points. This matrix equation corresponds to a system of linear algebraic equations with the unknown Euler coefficients. By solving this system, the unknown Euler coefficients of the solution are found. Some numerical examples are given and comparisons with other methods are made in order to demonstrate the applicability and validity of the proposed method.

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-Approximate polynomial solutions for the multi-pantograph equation with variable coefficients

Cited by 6 publications

References 20 publications

A novel approach to construct the adjoint problem for a first-order functional integro-differential equation with general nonlocal condition

A novel approach to construct the adjoint problem for a first-order functional integro-differential equation with general nonlocal condition

A new collocation method based on Euler polynomials for solution of generalized pantograph equations

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