S‎pectral method ‎‎for third-kind Volterra integral ‎equation

Authors

  • Haleh Tajadodi University of Sistan and Baluchestan

DOI:

https://doi.org/10.30495/jme.v15i0.2221

Keywords:

T‎hird-kind Volterra integral ‎equation‎‎, ‎Boubaker ‎polynomials‎‎, ‎O‎perational ‎matrix.‎

Abstract

T‎his present ‎work ‎will‎ ‎focus ‎on‎ ‎the ‎spectral ‎approach ‎to‎ a class ‎of‎ third-kind Volterra integral ‎equation ‎by means of the ‎Boubaker ‎polynomials as basis ‎function‎. ‎In this ‎‎approach ‎the ‎operational matrix of ‎fractional ‎integration ‎and the operational matrix of ‎multiplication ‎are utilized‎‎. ‎‎

The ‎strategy ‎‎‎‎that ‎adopts here ‎is‎ ‎expanding‎ the unknown function in terms of ‎Boubaker ‎polynomials with unknown ‎coefficients. Then, ‎by ‎using ‎‎the ‎given ‎the ‎operational ‎matrices‎, ‎the ‎problem ‎under ‎study‎ ‎is‎ ‎reduced‎ to a problem ‎easier to ‎solve ‎‎‎‎in the unknown ‎coefficients.‎ T‎he error ‎bound‎ of the ‎suggested ‎approximations ‎is‎ ‎investigated‎. ‎Some‎ examples are implemented to ‎display‎ the efficiency and ‎applicability‎ of the ‎recommended ‎scheme‎.‎

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Published

2022-03-03

Issue

Vol. 15

Section

Vol. 15, No. 5, (2021)

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