Using of PQWs for solving NFID in the complex plane

Abstract We approximate the solution of the nonlinear Fredholm integro-differential equation (NFID) in the complex plane by periodic quasi-wavelets (PQWs). This kind of wavelets possesses orthonormality properties, the numbers of terms in the decomposition and reconstruction formulas are strictly li...

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Main Authors:	M. Erfanian, H. Zeidabadi, M. Parsamanesh
Format:	Article
Language:	English
Published:	SpringerOpen 2020-01-01
Series:	Advances in Difference Equations
Subjects:	Nonlinear integro Fredholm integral equation PQWs B-spline functions complex plane
Online Access:	https://doi.org/10.1186/s13662-020-2528-z

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spelling	doaj-3e4901d768c2468bb82c952cd7f7bb8f2021-01-31T16:33:09ZengSpringerOpenAdvances in Difference Equations1687-18472020-01-012020111310.1186/s13662-020-2528-zUsing of PQWs for solving NFID in the complex planeM. Erfanian0H. Zeidabadi1M. Parsamanesh2Department of Science, School of Mathematical Sciences, University of ZabolFaculty of Engineering, Sabzevar University of New TechnologyDepartment of Science, School of Mathematical Sciences, University of ZabolAbstract We approximate the solution of the nonlinear Fredholm integro-differential equation (NFID) in the complex plane by periodic quasi-wavelets (PQWs). This kind of wavelets possesses orthonormality properties, the numbers of terms in the decomposition and reconstruction formulas are strictly limited, and the localization is not emphasized. To the best of our knowledge, there are no numerical methods to obtain the solution of the NFID by PQWs. Here, we attempt to obtain the numerical solution of the NFID based on B-spline functions. Finally, the simulation results are shown for three examples.https://doi.org/10.1186/s13662-020-2528-zNonlinear integro Fredholm integral equationPQWsB-spline functionscomplex plane
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	M. Erfanian H. Zeidabadi M. Parsamanesh
spellingShingle	M. Erfanian H. Zeidabadi M. Parsamanesh Using of PQWs for solving NFID in the complex plane Advances in Difference Equations Nonlinear integro Fredholm integral equation PQWs B-spline functions complex plane
author_facet	M. Erfanian H. Zeidabadi M. Parsamanesh
author_sort	M. Erfanian
title	Using of PQWs for solving NFID in the complex plane
title_short	Using of PQWs for solving NFID in the complex plane
title_full	Using of PQWs for solving NFID in the complex plane
title_fullStr	Using of PQWs for solving NFID in the complex plane
title_full_unstemmed	Using of PQWs for solving NFID in the complex plane
title_sort	using of pqws for solving nfid in the complex plane
publisher	SpringerOpen
series	Advances in Difference Equations
issn	1687-1847
publishDate	2020-01-01
description	Abstract We approximate the solution of the nonlinear Fredholm integro-differential equation (NFID) in the complex plane by periodic quasi-wavelets (PQWs). This kind of wavelets possesses orthonormality properties, the numbers of terms in the decomposition and reconstruction formulas are strictly limited, and the localization is not emphasized. To the best of our knowledge, there are no numerical methods to obtain the solution of the NFID by PQWs. Here, we attempt to obtain the numerical solution of the NFID based on B-spline functions. Finally, the simulation results are shown for three examples.
topic	Nonlinear integro Fredholm integral equation PQWs B-spline functions complex plane
url	https://doi.org/10.1186/s13662-020-2528-z
work_keys_str_mv	AT merfanian usingofpqwsforsolvingnfidinthecomplexplane AT hzeidabadi usingofpqwsforsolvingnfidinthecomplexplane AT mparsamanesh usingofpqwsforsolvingnfidinthecomplexplane
_version_	1724316287936495616

Using of PQWs for solving NFID in the complex plane

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