Application of Wavelet Transform to Urysohn-Type Equations

V. Lukianenko (), M. Kozlova and V. Belozub
Additional contact information
V. Lukianenko: Institute of Physics and Technology, V.I. Vernadsky Crimean Federal University, Simferopol 295007, Russia
M. Kozlova: Institute of Physics and Technology, V.I. Vernadsky Crimean Federal University, Simferopol 295007, Russia
V. Belozub: Institute of Physics and Technology, V.I. Vernadsky Crimean Federal University, Simferopol 295007, Russia

Mathematics, 2023, vol. 11, issue 18, 1-16

Abstract: This paper deals with convolution-type Urysohn equations of the first kind. Finding a solution for such equations is an ill-posed problem. For it to be solved, regularization algorithms and the continuous wavelet transform are used. Similar to the Fourier transform, the continuous wavelet transform is applied to convolution-type equations (based on the Fourier and wavelet transforms) and to Urysohn equations with unknown shift. The wavelet transform is preferable for the cases with approximated right-hand sides and for type 1 equations. We demonstrated that the application of the wavelet transform to Urysohn-type equations with unknown shift translates into a solution of a nonlinear equation with an oscillating kernel. Depending on the availability of a priori information, a combination of regularization and iterative algorithms with the use of close equations are effective for solving convolution-type equations based on the continuous wavelet transform and Urysohn equation.

Keywords: convolution-type Urysohn equations of the first kind; ill-posed problem; regularization algorithms; the continuous wavelet transform (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/18/3999/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/18/3999/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:18:p:3999-:d:1244091

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().