Solution of the Nonlinear Mixed Volterra-Fredholm Integral Equations by Hybrid of Block-Pulse Functions and Bernoulli Polynomials

A new numerical method for solving the nonlinear mixed Volterra-Fredholm integral equations is presented. This method is based upon hybrid functions approximation. The properties of hybrid functions consisting of block-pulse functions and Bernoulli polynomials are presented. The operational matrices...

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Detalles Bibliográficos
Autores principales: Mashayekhi, S., Razzaghi, M., Tripak, O.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Hindawi Publishing Corporation 2014
Materias:
Research Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3913454/
https://www.ncbi.nlm.nih.gov/pubmed/24523638
http://dx.doi.org/10.1155/2014/413623
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author Mashayekhi, S.
Razzaghi, M.
Tripak, O.
author_facet Mashayekhi, S.
Razzaghi, M.
Tripak, O.
author_sort Mashayekhi, S.
collection PubMed
description A new numerical method for solving the nonlinear mixed Volterra-Fredholm integral equations is presented. This method is based upon hybrid functions approximation. The properties of hybrid functions consisting of block-pulse functions and Bernoulli polynomials are presented. The operational matrices of integration and product are given. These matrices are then utilized to reduce the nonlinear mixed Volterra-Fredholm integral equations to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.
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spelling pubmed-39134542014-02-12 Solution of the Nonlinear Mixed Volterra-Fredholm Integral Equations by Hybrid of Block-Pulse Functions and Bernoulli Polynomials Mashayekhi, S. Razzaghi, M. Tripak, O. ScientificWorldJournal Research Article A new numerical method for solving the nonlinear mixed Volterra-Fredholm integral equations is presented. This method is based upon hybrid functions approximation. The properties of hybrid functions consisting of block-pulse functions and Bernoulli polynomials are presented. The operational matrices of integration and product are given. These matrices are then utilized to reduce the nonlinear mixed Volterra-Fredholm integral equations to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique. Hindawi Publishing Corporation 2014-01-12 /pmc/articles/PMC3913454/ /pubmed/24523638 http://dx.doi.org/10.1155/2014/413623 Text en Copyright © 2014 S. Mashayekhi et al. https://creativecommons.org/licenses/by/3.0/ This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
spellingShingle Research Article
Mashayekhi, S.
Razzaghi, M.
Tripak, O.
Solution of the Nonlinear Mixed Volterra-Fredholm Integral Equations by Hybrid of Block-Pulse Functions and Bernoulli Polynomials
title Solution of the Nonlinear Mixed Volterra-Fredholm Integral Equations by Hybrid of Block-Pulse Functions and Bernoulli Polynomials
title_full Solution of the Nonlinear Mixed Volterra-Fredholm Integral Equations by Hybrid of Block-Pulse Functions and Bernoulli Polynomials
title_fullStr Solution of the Nonlinear Mixed Volterra-Fredholm Integral Equations by Hybrid of Block-Pulse Functions and Bernoulli Polynomials
title_full_unstemmed Solution of the Nonlinear Mixed Volterra-Fredholm Integral Equations by Hybrid of Block-Pulse Functions and Bernoulli Polynomials
title_short Solution of the Nonlinear Mixed Volterra-Fredholm Integral Equations by Hybrid of Block-Pulse Functions and Bernoulli Polynomials
title_sort solution of the nonlinear mixed volterra-fredholm integral equations by hybrid of block-pulse functions and bernoulli polynomials
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3913454/
https://www.ncbi.nlm.nih.gov/pubmed/24523638
http://dx.doi.org/10.1155/2014/413623
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