Numerical Treatment of Abel’s Integral Equations Via Chelyshkov Wavelets Collocation Technique
This study presents a method to solve weakly singular Volterra integral equations using an approximation approach. The method relies on Chelyshkov wavelet polynomials. The characteristics of the Chelyshkov wavelet are presented. By employing these polynomials, the singular Volterra integral equation...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
REA Press
2024-09-01
|
| Series: | Computational Algorithms and Numerical Dimensions |
| Subjects: | |
| Online Access: | https://www.journal-cand.com/article_205104_45048f95e89b8f9086e5ebc4c17b79a4.pdf |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832580008776826880 |
|---|---|
| author | Youssef Esmaiel Magdi El-Azab Galal El-Baghdady |
| author_facet | Youssef Esmaiel Magdi El-Azab Galal El-Baghdady |
| author_sort | Youssef Esmaiel |
| collection | DOAJ |
| description | This study presents a method to solve weakly singular Volterra integral equations using an approximation approach. The method relies on Chelyshkov wavelet polynomials. The characteristics of the Chelyshkov wavelet are presented. By employing these polynomials, the singular Volterra integral equation is transformed into a set of algebraic equations that need to be solved. Subsequently, numerical analysis is introduced, followed by some examples and a comparison of them with existing methods to demonstrate the soundness and practicality of our method. |
| format | Article |
| id | doaj-art-17dcd3712f2c4c34903349cc445b2787 |
| institution | Kabale University |
| issn | 2980-7646 2980-9320 |
| language | English |
| publishDate | 2024-09-01 |
| publisher | REA Press |
| record_format | Article |
| series | Computational Algorithms and Numerical Dimensions |
| spelling | doaj-art-17dcd3712f2c4c34903349cc445b27872025-01-30T11:23:24ZengREA PressComputational Algorithms and Numerical Dimensions2980-76462980-93202024-09-013324325110.22105/cand.2024.477720.1112205104Numerical Treatment of Abel’s Integral Equations Via Chelyshkov Wavelets Collocation TechniqueYoussef Esmaiel0Magdi El-Azab1Galal El-Baghdady2Department of Mathematics & Engineering Physics, Faculty of Engineering, Mansoura University, Egypt.Department of Mathematics & Engineering Physics, Faculty of Engineering, Mansoura University, Egypt.Department of Mathematics & Engineering Physics, Faculty of Engineering, Mansoura University, Egypt.This study presents a method to solve weakly singular Volterra integral equations using an approximation approach. The method relies on Chelyshkov wavelet polynomials. The characteristics of the Chelyshkov wavelet are presented. By employing these polynomials, the singular Volterra integral equation is transformed into a set of algebraic equations that need to be solved. Subsequently, numerical analysis is introduced, followed by some examples and a comparison of them with existing methods to demonstrate the soundness and practicality of our method.https://www.journal-cand.com/article_205104_45048f95e89b8f9086e5ebc4c17b79a4.pdfchelyshkov waveletssingular volterra integral equationsabel's integral equationscollocation methodresidual error |
| spellingShingle | Youssef Esmaiel Magdi El-Azab Galal El-Baghdady Numerical Treatment of Abel’s Integral Equations Via Chelyshkov Wavelets Collocation Technique Computational Algorithms and Numerical Dimensions chelyshkov wavelets singular volterra integral equations abel's integral equations collocation method residual error |
| title | Numerical Treatment of Abel’s Integral Equations Via Chelyshkov Wavelets Collocation Technique |
| title_full | Numerical Treatment of Abel’s Integral Equations Via Chelyshkov Wavelets Collocation Technique |
| title_fullStr | Numerical Treatment of Abel’s Integral Equations Via Chelyshkov Wavelets Collocation Technique |
| title_full_unstemmed | Numerical Treatment of Abel’s Integral Equations Via Chelyshkov Wavelets Collocation Technique |
| title_short | Numerical Treatment of Abel’s Integral Equations Via Chelyshkov Wavelets Collocation Technique |
| title_sort | numerical treatment of abel s integral equations via chelyshkov wavelets collocation technique |
| topic | chelyshkov wavelets singular volterra integral equations abel's integral equations collocation method residual error |
| url | https://www.journal-cand.com/article_205104_45048f95e89b8f9086e5ebc4c17b79a4.pdf |
| work_keys_str_mv | AT youssefesmaiel numericaltreatmentofabelsintegralequationsviachelyshkovwaveletscollocationtechnique AT magdielazab numericaltreatmentofabelsintegralequationsviachelyshkovwaveletscollocationtechnique AT galalelbaghdady numericaltreatmentofabelsintegralequationsviachelyshkovwaveletscollocationtechnique |