Author First name, Last name, Institution

Mutaz Mohammad, Zayed University

ORCID Identifiers

0000-0003-0976-6021

Document Type

Article

Source of Publication

Entropy

Publication Date

11-1-2019

Abstract

© 2019 by the authors. Framelets theory has been well studied in many applications in image processing, data recovery and computational analysis due to the key properties of framelets such as sparse representation and accuracy in coefficients recovery in the area of numerical and computational theory. This work is devoted to shedding some light on the benefits of using such framelets in the area of numerical computations of integral equations. We introduce a new numerical method for solving Volterra integral equations. It is based on pseudo-spline quasi-affine tight framelet systems generated via the oblique extension principles. The resulting system is converted into matrix equations via these generators. We present examples of the generated pseudo-splines quasi-affine tight framelet systems. Some numerical results to validate the proposed method are presented to illustrate the efficiency and accuracy of the method.

ISSN

1099-4300

Publisher

MDPI AG

Volume

21

Issue

11

Disciplines

Life Sciences

Keywords

Biorthogonal wavelets, Multiresolution analysis, Oblique extension principle, Pseudo-splines, Quasi-affine systems, Volterra integral equations

Scopus ID

85075440565

Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Indexed in Scopus

yes

Open Access

yes

Open Access Type

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

Included in

Life Sciences Commons

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