Document Type

Article

Source of Publication

Alexandria Engineering Journal

Publication Date

8-1-2020

Abstract

© 2020 Faculty of Engineering, Alexandria University Tight framelet system is a recently developed tool in applied mathematics. Framelets, due to their nature, are widely used in the area of image manipulation, data compression, numerical analysis, engineering mathematical problems such as inverse problems, visco-elasticity or creep problems, and many more. In this manuscript we provide a numerical solution of important weakly singular type of Volterra - Fredholm integral equations WSVFIEs using the collocation type quasi-affine biorthogonal method. We present a new computational method based on special B-spline tight framelets and use it to introduce our numerical scheme. The method provides a robust solution for the given WSVFIE by using the resulting matrices based on these biorthogonal wavelet. We demonstrate the validity and accuracy of the proposed method by some numerical examples.

ISSN

1110-0168

Publisher

Elsevier B.V.

Volume

59

Issue

4

First Page

2181

Last Page

2191

Disciplines

Mathematics

Keywords

B-splines, Quasi-affine system, Tight framelets, Unitary extension principle, Weakly singular Volterra- Fredholm integral equations

Scopus ID

85079888861

Indexed in Scopus

yes

Open Access

yes

Open Access Type

Gold: This publication is openly available in an open access journal/series

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Included in

Mathematics Commons

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