Collocation and residual correction

Oliveira, Fernanda

doi:10.1007/bf01395986

Cited by 87 publications

(54 citation statements)

References 2 publications

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“…In this section, by using the residual error estimation for the Tau method [36,37] and the residual correction method [38,39], we develop an efficient error estimation for the exponential polynomial approximation and also, a technique to obtain the corrected solution (high accuracy of solution) of the problem (1), (2). For our purpose, we can define the residual function for the present method as…”

Section: Error Estimation Based On Residual Function and Improvement mentioning

confidence: 99%

An exponential approximation for solutions of generalized pantograph-delay differential equations

Yüzbaşı

Sezer

2013

Applied Mathematical Modelling

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a b s t r a c tIn this paper, a new matrix method based on exponential polynomials and collocation points is proposed for solutions of pantograph equations with linear functional arguments under the mixed conditions. Also, an error analysis technique based on residual function is developed for the suggested method. Some examples are given to demonstrate the validity and applicability of the method and the comparisons are made with existing results.

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Section: Error Estimation Based On Residual Function and Improvement mentioning

confidence: 99%

An exponential approximation for solutions of generalized pantograph-delay differential equations

Yüzbaşı

Sezer

2013

Applied Mathematical Modelling

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“…In this section, we will give an error estimation for the Morgan-Voyce polynomial solution (4) with the residual error function [23][24][25][26] and will improve the Morgan-Voyce polynomial solution (4) with the help of the residual error function. For this purpose, we get the residual function of the Morgan-Voyce collocation method as…”

Section: Residual Correction and Error Estimationmentioning

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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“…Also, this procedure is used to obtain the improved solution of the problem (4,5) according to the direct Jacobi polynomial solution. For this purpose, we use the residual correction technique [31,32] and error estimation by the known Tau method [33,34].…”

Section: Error Analysismentioning

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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Collocation and residual correction

Cited by 87 publications

References 2 publications

An exponential approximation for solutions of generalized pantograph-delay differential equations

An exponential approximation for solutions of generalized pantograph-delay differential 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

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