Polynomial solution of high-order linear Fredholm integro-differential equations with constant coefficients

Kurt, Nurcan; Sezer, Mehmet

doi:10.1016/j.jfranklin.2008.04.016

Cited by 71 publications

(41 citation statements)

References 26 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%

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%

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

İlhan¹

2017

ntmsci

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“…(4) under the mixed conditions (5), we replace the row matrix (31) by last n rows of the augmented matrix (30), which yields the new matrix equation form written as follow…”

Section: Methods Of Solutionmentioning

confidence: 99%

“…This function can be written using the truncated Taylor Series [30] and the truncated orthogonal Jacobi series, respectively, as…”

Section: Fundamental Matrix Relationsmentioning

confidence: 99%

Improved Jacobi matrix method for the numerical solution of Fredholm integro-differential-difference equations

Bahşı

Çevik

et al. 2016

Math Sci

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This study is aimed to develop a new matrix method, which is used an alternative numerical method to the other method for the high-order linear Fredholm integro-differential-difference equation with variable coefficients. This matrix method is based on orthogonal Jacobi polynomials and using collocation points. The improved Jacobi polynomial solution is obtained by summing up the basic Jacobi polynomial solution and the error estimation function. By comparing the results, it is shown that the improved Jacobi polynomial solution gives better results than the direct Jacobi polynomial solution, and also, than some other known methods. The advantage of this method is that Jacobi polynomials comprise all of the Legendre, Chebyshev, and Gegenbauer polynomials and, therefore, is the comprehensive polynomial solution technique

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“…If max 10 −k q = 10 −k (k positive integer) is prescribed, then the truncation limit N is increased until the difference E i (x q ) at each of the points becomes smaller than the prescribed 10 −k , see [10,11,22,23]. On the other hand, the error can be estimated by the function…”

Section: Accuracy Of Solutionmentioning

confidence: 99%

Numerical Solutions of Systems of High-Order Linear Differential-Difference Equations with Bessel Polynomial Bases

Yüzbaşı

Şahı̇n

Yıldırımb

2011

Zeitschrift Für Naturforschung A

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In this paper, a numerical matrix method, which is based on collocation points, is presented for the approximate solution of a system of high-order linear differential-difference equations with variable coefficients under the mixed conditions in terms of Bessel polynomials. Numerical examples are included to demonstrate the validity and applicability of the technique and comparisons are made with existing results. The results show the efficiency and accuracy of the present work. All of the numerical computations have been performed on computer using a program written in MATLAB v7.6.0 (R2008a).

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Polynomial solution of high-order linear Fredholm integro-differential equations with constant coefficients

Cited by 71 publications

References 26 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

Improved Jacobi matrix method for the numerical solution of Fredholm integro-differential-difference equations

Numerical Solutions of Systems of High-Order Linear Differential-Difference Equations with Bessel Polynomial Bases

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