Rational approximation for solving Fredholm integro-differential equations by new algorithm
In this article, we used a novel semi-analytical approach, named the optimal auxiliary function method (OAFM), to solve integro-differential equations (IDEs). The OAFM includes an auxiliary function and convergence control parameters, which expedite the convergence of the method. To apply the propos...
| Main Authors: | , , , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2023-10-01
|
| Series: | Open Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/phys-2022-0181 |
| _version_ | 1797653362435424256 |
|---|---|
| author | Nawaz Rashid Sumera Zada Laiq Ayaz Muhammad Ahmad Hijaz Awwad Fuad A. Ismail Emad A. A. |
| author_facet | Nawaz Rashid Sumera Zada Laiq Ayaz Muhammad Ahmad Hijaz Awwad Fuad A. Ismail Emad A. A. |
| author_sort | Nawaz Rashid |
| collection | DOAJ |
| description | In this article, we used a novel semi-analytical approach, named the optimal auxiliary function method (OAFM), to solve integro-differential equations (IDEs). The OAFM includes an auxiliary function and convergence control parameters, which expedite the convergence of the method. To apply the proposed method, some assumptions regarding small or large parameters in the problem are necessary. We present numerical outcomes acquired via the OAFM alongside those obtained from other numerical techniques in tables. Furthermore, we demonstrate the efficacy and ease of implementing the proposed method for various IDEs using 2D graphs. |
| first_indexed | 2024-03-11T16:43:35Z |
| format | Article |
| id | doaj.art-ae886c2e5b6b45f4953e2bee6c38d065 |
| institution | Directory Open Access Journal |
| issn | 2391-5471 |
| language | English |
| last_indexed | 2024-03-11T16:43:35Z |
| publishDate | 2023-10-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Physics |
| spelling | doaj.art-ae886c2e5b6b45f4953e2bee6c38d0652023-10-23T07:51:02ZengDe GruyterOpen Physics2391-54712023-10-0121130799610.1515/phys-2022-0181Rational approximation for solving Fredholm integro-differential equations by new algorithmNawaz Rashid0Sumera1Zada Laiq2Ayaz Muhammad3Ahmad Hijaz4Awwad Fuad A.5Ismail Emad A. A.6UniSa STEM, University of South Australia, Adelaide, AustraliaDepartment of Mathematics, Abdul Wali Khan University Mardan Khyber Pakhtunkhwa, Mardan, PakistanDepartment of Mathematics, Abdul Wali Khan University Mardan Khyber Pakhtunkhwa, Mardan, PakistanDepartment of Mathematics, Abdul Wali Khan University Mardan Khyber Pakhtunkhwa, Mardan, PakistanOperational Research Center in Healthcare, Near East University, Near East Boulevard, PC: 99138Nicosia/Mersin 10, TurkeyDepartment of Quantitative analysis, College of Business Administration, King Saud University, P.O. Box 71115, Riyadh 11587, Saudi ArabiaDepartment of Quantitative analysis, College of Business Administration, King Saud University, P.O. Box 71115, Riyadh 11587, Saudi ArabiaIn this article, we used a novel semi-analytical approach, named the optimal auxiliary function method (OAFM), to solve integro-differential equations (IDEs). The OAFM includes an auxiliary function and convergence control parameters, which expedite the convergence of the method. To apply the proposed method, some assumptions regarding small or large parameters in the problem are necessary. We present numerical outcomes acquired via the OAFM alongside those obtained from other numerical techniques in tables. Furthermore, we demonstrate the efficacy and ease of implementing the proposed method for various IDEs using 2D graphs.https://doi.org/10.1515/phys-2022-0181optimal auxiliary function methodexact solutionsfredholm integro-differential equations |
| spellingShingle | Nawaz Rashid Sumera Zada Laiq Ayaz Muhammad Ahmad Hijaz Awwad Fuad A. Ismail Emad A. A. Rational approximation for solving Fredholm integro-differential equations by new algorithm Open Physics optimal auxiliary function method exact solutions fredholm integro-differential equations |
| title | Rational approximation for solving Fredholm integro-differential equations by new algorithm |
| title_full | Rational approximation for solving Fredholm integro-differential equations by new algorithm |
| title_fullStr | Rational approximation for solving Fredholm integro-differential equations by new algorithm |
| title_full_unstemmed | Rational approximation for solving Fredholm integro-differential equations by new algorithm |
| title_short | Rational approximation for solving Fredholm integro-differential equations by new algorithm |
| title_sort | rational approximation for solving fredholm integro differential equations by new algorithm |
| topic | optimal auxiliary function method exact solutions fredholm integro-differential equations |
| url | https://doi.org/10.1515/phys-2022-0181 |
| work_keys_str_mv | AT nawazrashid rationalapproximationforsolvingfredholmintegrodifferentialequationsbynewalgorithm AT sumera rationalapproximationforsolvingfredholmintegrodifferentialequationsbynewalgorithm AT zadalaiq rationalapproximationforsolvingfredholmintegrodifferentialequationsbynewalgorithm AT ayazmuhammad rationalapproximationforsolvingfredholmintegrodifferentialequationsbynewalgorithm AT ahmadhijaz rationalapproximationforsolvingfredholmintegrodifferentialequationsbynewalgorithm AT awwadfuada rationalapproximationforsolvingfredholmintegrodifferentialequationsbynewalgorithm AT ismailemadaa rationalapproximationforsolvingfredholmintegrodifferentialequationsbynewalgorithm |