Numerical solution of nonlinear complex integral equations using quasi- wavelets
In this paper, we introduced a numerical approach for estimating the solutions of nonlinear Fredholm integral equations in the complex plane. The main problem was transformed into a novel integral equation, which simplified the computation of integrals derived from the discretization technique. The...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2024-12-01
|
| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241638 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832590741544632320 |
|---|---|
| author | Ahmed Ayad Khudhair Saeed Sohrabi Hamid Ranjbar |
| author_facet | Ahmed Ayad Khudhair Saeed Sohrabi Hamid Ranjbar |
| author_sort | Ahmed Ayad Khudhair |
| collection | DOAJ |
| description | In this paper, we introduced a numerical approach for estimating the solutions of nonlinear Fredholm integral equations in the complex plane. The main problem was transformed into a novel integral equation, which simplified the computation of integrals derived from the discretization technique. The combination of the standard collocation method with periodic quasi-wavelets, as well as their fundamental properties, was utilized to convert the solution of the newly formulated integral equation into a nonlinear complex system of algebraic equations. The convergence properties of the scheme were also presented. Finally, several numerical examples were provided to demonstrate the efficiency and precision of our proposed approach, which also confirmed its superiority over polynomial collocation methods. |
| format | Article |
| id | doaj-art-4ccbcbdeb49f4c549486b7c5889360b6 |
| institution | Kabale University |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-4ccbcbdeb49f4c549486b7c5889360b62025-01-23T07:53:25ZengAIMS PressAIMS Mathematics2473-69882024-12-01912343873440510.3934/math.20241638Numerical solution of nonlinear complex integral equations using quasi- waveletsAhmed Ayad Khudhair0Saeed Sohrabi1Hamid Ranjbar2Department of Mathematics, Faculty of Science, Urmia University, Urmia 57561-51818, IranDepartment of Mathematics, Faculty of Science, Urmia University, Urmia 57561-51818, IranDepartment of Mathematics, Faculty of Science, Urmia University, Urmia 57561-51818, IranIn this paper, we introduced a numerical approach for estimating the solutions of nonlinear Fredholm integral equations in the complex plane. The main problem was transformed into a novel integral equation, which simplified the computation of integrals derived from the discretization technique. The combination of the standard collocation method with periodic quasi-wavelets, as well as their fundamental properties, was utilized to convert the solution of the newly formulated integral equation into a nonlinear complex system of algebraic equations. The convergence properties of the scheme were also presented. Finally, several numerical examples were provided to demonstrate the efficiency and precision of our proposed approach, which also confirmed its superiority over polynomial collocation methods.https://www.aimspress.com/article/doi/10.3934/math.20241638collocation methodhammerstein integral equationperiodic quasi-waveletscomplex planeconvergence |
| spellingShingle | Ahmed Ayad Khudhair Saeed Sohrabi Hamid Ranjbar Numerical solution of nonlinear complex integral equations using quasi- wavelets AIMS Mathematics collocation method hammerstein integral equation periodic quasi-wavelets complex plane convergence |
| title | Numerical solution of nonlinear complex integral equations using quasi- wavelets |
| title_full | Numerical solution of nonlinear complex integral equations using quasi- wavelets |
| title_fullStr | Numerical solution of nonlinear complex integral equations using quasi- wavelets |
| title_full_unstemmed | Numerical solution of nonlinear complex integral equations using quasi- wavelets |
| title_short | Numerical solution of nonlinear complex integral equations using quasi- wavelets |
| title_sort | numerical solution of nonlinear complex integral equations using quasi wavelets |
| topic | collocation method hammerstein integral equation periodic quasi-wavelets complex plane convergence |
| url | https://www.aimspress.com/article/doi/10.3934/math.20241638 |
| work_keys_str_mv | AT ahmedayadkhudhair numericalsolutionofnonlinearcomplexintegralequationsusingquasiwavelets AT saeedsohrabi numericalsolutionofnonlinearcomplexintegralequationsusingquasiwavelets AT hamidranjbar numericalsolutionofnonlinearcomplexintegralequationsusingquasiwavelets |