A Taylor method for numerical solution of generalized pantograph equations with linear functional argument

Sezer, Mehmet; Akyüz-Daşcıoğlu, Ayşegül

doi:10.1016/j.cam.2005.12.015

Cited by 90 publications

(84 citation statements)

References 22 publications

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“…(1), we replace the row matrice (13) by the last one row of the matrix (12), so have the new augmented matrix [15,16,17]…”

Section: Methods Of Solutionmentioning

confidence: 99%

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An improved Morgan-voyce collocation method for numerical solution of multi-pantograph equations

İlhan¹

2017

ntmsci

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Abstract:In this article, an improved collocation method based on the Morgan-Voyce polynomials for the approximates solution of multi-pantograph equations is introduced. The method is based upon the improvement of Morgan-Voyce polynomial solutions with the aid of the residual error function. First, the Morgan-Voyce collocation method is applied to the multi-pantograph equations and then Morgan-Voyce polynomial solutions are obtained. Second, an error problem is constructed by means of the residual error function and this error problem is solved by using the Morgan-Voyce collocation method. By summing the Morgan-Voyce polynomial solutions of the original problem and the error problem, we have the improved Morgan-Voyce polynomial solutions. When the exact solution of problem is not known, the absolute error can then be approximately computed by the Morgan-Voyce polynomial solution of the error problem. Numerical examples that the pertinent features of the method are presented. We have applied all of the numerical computations on computer using a program written in MATLAB.

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“…(1), we replace the row matrice (13) by the last one row of the matrix (12), so have the new augmented matrix [15,16,17]…”

Section: Methods Of Solutionmentioning

confidence: 99%

“…The purpose of this work is to apply Morgan-Voyce polynomials to the nonhomogenous and the homogenous multi-pantograph equations with variable coefficients, which is the extension of the pantograph equations given in [5,16].…”

Section: Introductionmentioning

confidence: 99%

An improved Morgan-voyce collocation method for numerical solution of multi-pantograph equations

İlhan¹

2017

ntmsci

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“…The problems were considered in [13,16] without error estimation. In this case, we can see the main advantage of the residual correction technique, which is that we can estimate the error of the approximate solution when the exact solution is not of closed form.…”

Section: The Exact Solution Of the Problem Ismentioning

confidence: 99%

“…Brunner et al [4] used the Galerkin methods for solutions of delayed differential equations of pantograph type. In [1,13,15,20], the collocation methods were developed for functional equations with delays.…”

Section: Introductionmentioning

confidence: 99%

A Taylor operation method for solutions of generalized pantograph type delay differential equations

Yüzbaşı¹,

Ismailov²

2018

Turk J Math

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In this paper, a new operational matrix method based on the Taylor polynomials is presented to solve generalized pantograph type delay differential equations. The method is based on operational matrices of integration and product for Taylor polynomials. These matrices are obtained by using the best approximation of function by the Taylor polynomials. The advantage of the method is that the method does not require collocation points. By using the proposed method, the generalized pantograph equation problem is reduced to a system of linear algebraic equations. The solving of this system gives the coefficients of our solution. Numerical examples are given to demonstrate the accuracy of the technique and the numerical results show that the error of the present method is superior to that of other methods.The residual correction technique is used to improve the accuracy of the approximate solution and estimation of absolute error. The estimation aspect of the residual method is useful when the exact solution of the considered equation is unknown and this feature of the method is shown in numerical examples.

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“…The following second order delay differential [6,7,8] by Sezer et al and θ-method [4] by Liu and Li. Saadatmandi and Dehghan applied the variational iteration method in [5] and Yu in [15] as well.…”

Section: Introductionmentioning

confidence: 99%

Two Numerical Methods to Solve the Second Order Multi-pantograph Equation with Boundary Conditions

Ahmadinia¹,

Safari

2014

AMP

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In this article, we present two numerical methods to solve the second order multi-pantograph equation with boundary conditions. The multi-pantograph equation is converted to an integral equation then the integral equation is solved by two projective methods. Some properties of Chebyshev polynomials are employed to prove the convergence analysis of the two proposed methods. Finally, numerical examples also are given to illustrate the efficiency and validity of the two proposed methods.

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A Taylor method for numerical solution of generalized pantograph equations with linear functional argument

Cited by 90 publications

References 22 publications

An improved Morgan-voyce collocation method for numerical solution of multi-pantograph equations

An improved Morgan-voyce collocation method for numerical solution of multi-pantograph equations

A Taylor operation method for solutions of generalized pantograph type delay differential equations

Two Numerical Methods to Solve the Second Order Multi-pantograph Equation with Boundary Conditions

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