Approximate Solutions for a Class of Nonlinear Fredholm and Volterra Integro-Differential Equations Using the Polynomial Least Squares Method

We apply the polynomial least squares method to obtain approximate analytical solutions for a very general class of nonlinear Fredholm and Volterra integro-differential equations. The method is a relatively simple and straightforward one, but its precision for this type of equations is very high, a...

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Autores principales:	Bogdan Căruntu, Mădălina Sofia Paşca
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	Volterra and Fredholm nonlinear integro-differential equations approximate analytic polynomial solution polynomial least squares method Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/99765c6f1be5456e804227fa0939b9d8
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id	oai:doaj.org-article:99765c6f1be5456e804227fa0939b9d8
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spelling	oai:doaj.org-article:99765c6f1be5456e804227fa0939b9d82021-11-11T18:15:29ZApproximate Solutions for a Class of Nonlinear Fredholm and Volterra Integro-Differential Equations Using the Polynomial Least Squares Method10.3390/math92126922227-7390https://doaj.org/article/99765c6f1be5456e804227fa0939b9d82021-10-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/21/2692https://doaj.org/toc/2227-7390We apply the polynomial least squares method to obtain approximate analytical solutions for a very general class of nonlinear Fredholm and Volterra integro-differential equations. The method is a relatively simple and straightforward one, but its precision for this type of equations is very high, a fact that is illustrated by the numerical examples presented. The comparison with previous approximations computed for the included test problems emphasizes the method’s simplicity and accuracy.Bogdan CăruntuMădălina Sofia PaşcaMDPI AGarticleVolterra and Fredholm nonlinear integro-differential equationsapproximate analytic polynomial solutionpolynomial least squares methodMathematicsQA1-939ENMathematics, Vol 9, Iss 2692, p 2692 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Volterra and Fredholm nonlinear integro-differential equations approximate analytic polynomial solution polynomial least squares method Mathematics QA1-939
spellingShingle	Volterra and Fredholm nonlinear integro-differential equations approximate analytic polynomial solution polynomial least squares method Mathematics QA1-939 Bogdan Căruntu Mădălina Sofia Paşca Approximate Solutions for a Class of Nonlinear Fredholm and Volterra Integro-Differential Equations Using the Polynomial Least Squares Method
description	We apply the polynomial least squares method to obtain approximate analytical solutions for a very general class of nonlinear Fredholm and Volterra integro-differential equations. The method is a relatively simple and straightforward one, but its precision for this type of equations is very high, a fact that is illustrated by the numerical examples presented. The comparison with previous approximations computed for the included test problems emphasizes the method’s simplicity and accuracy.
format	article
author	Bogdan Căruntu Mădălina Sofia Paşca
author_facet	Bogdan Căruntu Mădălina Sofia Paşca
author_sort	Bogdan Căruntu
title	Approximate Solutions for a Class of Nonlinear Fredholm and Volterra Integro-Differential Equations Using the Polynomial Least Squares Method
title_short	Approximate Solutions for a Class of Nonlinear Fredholm and Volterra Integro-Differential Equations Using the Polynomial Least Squares Method
title_full	Approximate Solutions for a Class of Nonlinear Fredholm and Volterra Integro-Differential Equations Using the Polynomial Least Squares Method
title_fullStr	Approximate Solutions for a Class of Nonlinear Fredholm and Volterra Integro-Differential Equations Using the Polynomial Least Squares Method
title_full_unstemmed	Approximate Solutions for a Class of Nonlinear Fredholm and Volterra Integro-Differential Equations Using the Polynomial Least Squares Method
title_sort	approximate solutions for a class of nonlinear fredholm and volterra integro-differential equations using the polynomial least squares method
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/99765c6f1be5456e804227fa0939b9d8
work_keys_str_mv	AT bogdancaruntu approximatesolutionsforaclassofnonlinearfredholmandvolterraintegrodifferentialequationsusingthepolynomialleastsquaresmethod AT madalinasofiapasca approximatesolutionsforaclassofnonlinearfredholmandvolterraintegrodifferentialequationsusingthepolynomialleastsquaresmethod
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Approximate Solutions for a Class of Nonlinear Fredholm and Volterra Integro-Differential Equations Using the Polynomial Least Squares Method

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