Solving two-dimensional nonlinear fuzzy Volterra integral equations by homotopy analysis method

The purpose of the paper is to find an approximate solution of the two-dimensional nonlinear fuzzy Volterra integral equation, as homotopy analysis method (HAM) is applied. Studied equation is converted to a nonlinear system of Volterra integral equations in a crisp case. Using HAM we find approxima...

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Autor principal:	Georgieva Atanaska
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2021
Materias:	homotopy analysis method two-dimensional nonlinear fuzzy volterra integral equation convergence error estimation 41a25 45g10 65r20 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/a913e8e8b78943bf9358a11b8e6424f9
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id	oai:doaj.org-article:a913e8e8b78943bf9358a11b8e6424f9
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spelling	oai:doaj.org-article:a913e8e8b78943bf9358a11b8e6424f92021-12-05T14:10:45ZSolving two-dimensional nonlinear fuzzy Volterra integral equations by homotopy analysis method2391-466110.1515/dema-2021-0005https://doaj.org/article/a913e8e8b78943bf9358a11b8e6424f92021-04-01T00:00:00Zhttps://doi.org/10.1515/dema-2021-0005https://doaj.org/toc/2391-4661The purpose of the paper is to find an approximate solution of the two-dimensional nonlinear fuzzy Volterra integral equation, as homotopy analysis method (HAM) is applied. Studied equation is converted to a nonlinear system of Volterra integral equations in a crisp case. Using HAM we find approximate solution of this system and hence obtain an approximation for the fuzzy solution of the nonlinear fuzzy Volterra integral equation. The convergence of the proposed method is proved. An error estimate between the exact and the approximate solution is found. The validity and applicability of the HAM are illustrated by a numerical example.Georgieva AtanaskaDe Gruyterarticlehomotopy analysis methodtwo-dimensional nonlinear fuzzy volterra integral equationconvergenceerror estimation41a2545g1065r20MathematicsQA1-939ENDemonstratio Mathematica, Vol 54, Iss 1, Pp 11-24 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	homotopy analysis method two-dimensional nonlinear fuzzy volterra integral equation convergence error estimation 41a25 45g10 65r20 Mathematics QA1-939
spellingShingle	homotopy analysis method two-dimensional nonlinear fuzzy volterra integral equation convergence error estimation 41a25 45g10 65r20 Mathematics QA1-939 Georgieva Atanaska Solving two-dimensional nonlinear fuzzy Volterra integral equations by homotopy analysis method
description	The purpose of the paper is to find an approximate solution of the two-dimensional nonlinear fuzzy Volterra integral equation, as homotopy analysis method (HAM) is applied. Studied equation is converted to a nonlinear system of Volterra integral equations in a crisp case. Using HAM we find approximate solution of this system and hence obtain an approximation for the fuzzy solution of the nonlinear fuzzy Volterra integral equation. The convergence of the proposed method is proved. An error estimate between the exact and the approximate solution is found. The validity and applicability of the HAM are illustrated by a numerical example.
format	article
author	Georgieva Atanaska
author_facet	Georgieva Atanaska
author_sort	Georgieva Atanaska
title	Solving two-dimensional nonlinear fuzzy Volterra integral equations by homotopy analysis method
title_short	Solving two-dimensional nonlinear fuzzy Volterra integral equations by homotopy analysis method
title_full	Solving two-dimensional nonlinear fuzzy Volterra integral equations by homotopy analysis method
title_fullStr	Solving two-dimensional nonlinear fuzzy Volterra integral equations by homotopy analysis method
title_full_unstemmed	Solving two-dimensional nonlinear fuzzy Volterra integral equations by homotopy analysis method
title_sort	solving two-dimensional nonlinear fuzzy volterra integral equations by homotopy analysis method
publisher	De Gruyter
publishDate	2021
url	https://doaj.org/article/a913e8e8b78943bf9358a11b8e6424f9
work_keys_str_mv	AT georgievaatanaska solvingtwodimensionalnonlinearfuzzyvolterraintegralequationsbyhomotopyanalysismethod
_version_	1718371768375181312

Solving two-dimensional nonlinear fuzzy Volterra integral equations by homotopy analysis method

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