An Efficient Collocation Method for the Numerical Solutions of the Pantograph-Type Volterra Hammerstein Integral Equations and its Convergence Analysis

In this work, we consider a collocation method for solving the pantograph-type Volterra Hammerstein integral equations based on the first kind Chebyshev polynomials. We use the Lagrange interpolating polynomial to approximate the solution. The convergence of the presented method has been analyzed by...

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Main Authors: Hashem Saberi Najafi, Sayed Arsalan Sajjadi, Hossein Aminikhah
Format: Article
Language:English
Published: REA Press 2022-06-01
Series:Computational Algorithms and Numerical Dimensions
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Online Access:https://www.journal-cand.com/article_153956_f64d94f631f3223fc3a41a690c56d809.pdf
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author Hashem Saberi Najafi
Sayed Arsalan Sajjadi
Hossein Aminikhah
author_facet Hashem Saberi Najafi
Sayed Arsalan Sajjadi
Hossein Aminikhah
author_sort Hashem Saberi Najafi
collection DOAJ
description In this work, we consider a collocation method for solving the pantograph-type Volterra Hammerstein integral equations based on the first kind Chebyshev polynomials. We use the Lagrange interpolating polynomial to approximate the solution. The convergence of the presented method has been analyzed by over estimating for error. Finally, some illustrative examples are given to test the accuracy of the method. The presented method is compared with the Legendre Tau method.
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institution Kabale University
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publishDate 2022-06-01
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series Computational Algorithms and Numerical Dimensions
spelling doaj-art-e4d4f124e29f4a528e138680e68d4a4f2025-01-30T11:20:45ZengREA PressComputational Algorithms and Numerical Dimensions2980-76462980-93202022-06-0112617110.22105/cand.2022.153956153956An Efficient Collocation Method for the Numerical Solutions of the Pantograph-Type Volterra Hammerstein Integral Equations and its Convergence AnalysisHashem Saberi Najafi0Sayed Arsalan Sajjadi1Hossein Aminikhah2Department of Applied Mathematics, Ayandegan Institute of Higher Education, Tonekabon, Iran.Department of Applied Mathematics and Computer Science‎, ‎Faculty of Mathematical Sciences‎, ‎University of Guilan, Iran.Department of Applied Mathematics and Computer Science‎, ‎Faculty of Mathematical Sciences‎, ‎University of Guilan, Iran.In this work, we consider a collocation method for solving the pantograph-type Volterra Hammerstein integral equations based on the first kind Chebyshev polynomials. We use the Lagrange interpolating polynomial to approximate the solution. The convergence of the presented method has been analyzed by over estimating for error. Finally, some illustrative examples are given to test the accuracy of the method. The presented method is compared with the Legendre Tau method.https://www.journal-cand.com/article_153956_f64d94f631f3223fc3a41a690c56d809.pdfnumerical solutioncollocation methodpantograph-typevolterra hammerstein integral equationsconvergence analysis
spellingShingle Hashem Saberi Najafi
Sayed Arsalan Sajjadi
Hossein Aminikhah
An Efficient Collocation Method for the Numerical Solutions of the Pantograph-Type Volterra Hammerstein Integral Equations and its Convergence Analysis
Computational Algorithms and Numerical Dimensions
numerical solution
collocation method
pantograph-type
volterra hammerstein integral equations
convergence analysis
title An Efficient Collocation Method for the Numerical Solutions of the Pantograph-Type Volterra Hammerstein Integral Equations and its Convergence Analysis
title_full An Efficient Collocation Method for the Numerical Solutions of the Pantograph-Type Volterra Hammerstein Integral Equations and its Convergence Analysis
title_fullStr An Efficient Collocation Method for the Numerical Solutions of the Pantograph-Type Volterra Hammerstein Integral Equations and its Convergence Analysis
title_full_unstemmed An Efficient Collocation Method for the Numerical Solutions of the Pantograph-Type Volterra Hammerstein Integral Equations and its Convergence Analysis
title_short An Efficient Collocation Method for the Numerical Solutions of the Pantograph-Type Volterra Hammerstein Integral Equations and its Convergence Analysis
title_sort efficient collocation method for the numerical solutions of the pantograph type volterra hammerstein integral equations and its convergence analysis
topic numerical solution
collocation method
pantograph-type
volterra hammerstein integral equations
convergence analysis
url https://www.journal-cand.com/article_153956_f64d94f631f3223fc3a41a690c56d809.pdf
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