Haar wavelet collocation method for existence and numerical solutions of fourth-order integro-differential equations with bounded coefficients
In this article, Haar wavelet collocation method is applied for the solution of fourth-order integro-differential equations. Also, a fixed point approach is used to investigate the existence theory of solution to the considered problem. The fourth-order derivative is approximated using Haar function...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2025-04-01
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| Series: | Nonlinear Engineering |
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| Online Access: | https://doi.org/10.1515/nleng-2025-0125 |
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| author | Amin Rohul Nawaz Muhammad Shah Kamal Abdeljawad Thabet |
| author_facet | Amin Rohul Nawaz Muhammad Shah Kamal Abdeljawad Thabet |
| author_sort | Amin Rohul |
| collection | DOAJ |
| description | In this article, Haar wavelet collocation method is applied for the solution of fourth-order integro-differential equations. Also, a fixed point approach is used to investigate the existence theory of solution to the considered problem. The fourth-order derivative is approximated using Haar function. In addition, third-, second-, and first-order derivatives together with unknown functions are obtained by the process of successive integrations. On applying the Haar collocation method, the suggested problem of IDEs is transformed to a system of algebraic equations. The Gauss elimination scheme is used for the solution of linear algebraic equations. The precision, effectiveness, and convergence of the Haar approach are checked on some test problems. Different collocation and Gauss points are used to determine the absolute and root mean square errors. To demonstrate the applicability of the proposed method, an experimental rate of convergence is calculated, which is almost equal to 2. The method is accurate, easily applicable, and efficient. |
| format | Article |
| id | doaj-art-86223ff8e4454abda2d685b3878b1f4c |
| institution | OA Journals |
| issn | 2192-8029 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Nonlinear Engineering |
| spelling | doaj-art-86223ff8e4454abda2d685b3878b1f4c2025-08-20T02:20:03ZengDe GruyterNonlinear Engineering2192-80292025-04-0114110869110.1515/nleng-2025-0125Haar wavelet collocation method for existence and numerical solutions of fourth-order integro-differential equations with bounded coefficientsAmin Rohul0Nawaz Muhammad1Shah Kamal2Abdeljawad Thabet3Department of Mathematics, University of Peshawar, Khyber Pakhtunkhwa, 25120, PakistanDepartment of Mathematics, University of Peshawar, Khyber Pakhtunkhwa, 25120, PakistanDepartment of Mathematics and Sciences, Prince Sultan University, Riyadh, P.O. Box 11586, Saudi ArabiaDepartment of Mathematics and Sciences, Prince Sultan University, Riyadh, P.O. Box 11586, Saudi ArabiaIn this article, Haar wavelet collocation method is applied for the solution of fourth-order integro-differential equations. Also, a fixed point approach is used to investigate the existence theory of solution to the considered problem. The fourth-order derivative is approximated using Haar function. In addition, third-, second-, and first-order derivatives together with unknown functions are obtained by the process of successive integrations. On applying the Haar collocation method, the suggested problem of IDEs is transformed to a system of algebraic equations. The Gauss elimination scheme is used for the solution of linear algebraic equations. The precision, effectiveness, and convergence of the Haar approach are checked on some test problems. Different collocation and Gauss points are used to determine the absolute and root mean square errors. To demonstrate the applicability of the proposed method, an experimental rate of convergence is calculated, which is almost equal to 2. The method is accurate, easily applicable, and efficient.https://doi.org/10.1515/nleng-2025-0125integral equationsfixed point approachgauss elimination schemehaar wavelet |
| spellingShingle | Amin Rohul Nawaz Muhammad Shah Kamal Abdeljawad Thabet Haar wavelet collocation method for existence and numerical solutions of fourth-order integro-differential equations with bounded coefficients Nonlinear Engineering integral equations fixed point approach gauss elimination scheme haar wavelet |
| title | Haar wavelet collocation method for existence and numerical solutions of fourth-order integro-differential equations with bounded coefficients |
| title_full | Haar wavelet collocation method for existence and numerical solutions of fourth-order integro-differential equations with bounded coefficients |
| title_fullStr | Haar wavelet collocation method for existence and numerical solutions of fourth-order integro-differential equations with bounded coefficients |
| title_full_unstemmed | Haar wavelet collocation method for existence and numerical solutions of fourth-order integro-differential equations with bounded coefficients |
| title_short | Haar wavelet collocation method for existence and numerical solutions of fourth-order integro-differential equations with bounded coefficients |
| title_sort | haar wavelet collocation method for existence and numerical solutions of fourth order integro differential equations with bounded coefficients |
| topic | integral equations fixed point approach gauss elimination scheme haar wavelet |
| url | https://doi.org/10.1515/nleng-2025-0125 |
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