Direct solution of third-order linear integro-differential equation using Cubic B-Spline Method
Solving Volterra integro-differential equations with cubic B-splines offers a powerful, flexible numerical approach to model complex real-world systems, such as those in population dynamics or material science. The collocation method, based on the cubic B-spline approach, has been developed to solve...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Penerbit Universiti Kebangsaan Malaysia
2025
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| Online Access: | http://journalarticle.ukm.my/25772/ http://journalarticle.ukm.my/25772/1/113-132%20-.pdf |
| _version_ | 1848816445296738304 |
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| author | Hamida Ali, Norazak Senu, |
| author_facet | Hamida Ali, Norazak Senu, |
| author_sort | Hamida Ali, |
| building | UKM Institutional Repository |
| collection | Online Access |
| description | Solving Volterra integro-differential equations with cubic B-splines offers a powerful, flexible numerical approach to model complex real-world systems, such as those in population dynamics or material science. The collocation method, based on the cubic B-spline approach, has been developed to solve third-order linear Fredholm and Volterra integro-differential equations. cubic B-splines are often preferred over other interpolation and approximation techniques due to their smoothness, local control, numerical stability, and computational efficiency. This cubic Bspline method collocates both the solution and its derivatives. Meanwhile, the integral part is approximated using the GaussLegendre quadrature formula. A theoretical convergence analysis of the cubic B-spline method has been conducted and found that the order convergence is second order. The method was applied to six test examples, and the numerical solutions were compared with the corresponding analytical solutions. The maximum absolute error and mean square root error are decreased by increasing the number N. It has been found that the proposed method is efficient and capable of solving third-order linear integro-differential equations for different values of N. |
| first_indexed | 2025-11-15T01:05:59Z |
| format | Article |
| id | oai:generic.eprints.org:25772 |
| institution | Universiti Kebangasaan Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T01:05:59Z |
| publishDate | 2025 |
| publisher | Penerbit Universiti Kebangsaan Malaysia |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | oai:generic.eprints.org:257722025-08-15T03:47:26Z http://journalarticle.ukm.my/25772/ Direct solution of third-order linear integro-differential equation using Cubic B-Spline Method Hamida Ali, Norazak Senu, Solving Volterra integro-differential equations with cubic B-splines offers a powerful, flexible numerical approach to model complex real-world systems, such as those in population dynamics or material science. The collocation method, based on the cubic B-spline approach, has been developed to solve third-order linear Fredholm and Volterra integro-differential equations. cubic B-splines are often preferred over other interpolation and approximation techniques due to their smoothness, local control, numerical stability, and computational efficiency. This cubic Bspline method collocates both the solution and its derivatives. Meanwhile, the integral part is approximated using the GaussLegendre quadrature formula. A theoretical convergence analysis of the cubic B-spline method has been conducted and found that the order convergence is second order. The method was applied to six test examples, and the numerical solutions were compared with the corresponding analytical solutions. The maximum absolute error and mean square root error are decreased by increasing the number N. It has been found that the proposed method is efficient and capable of solving third-order linear integro-differential equations for different values of N. Penerbit Universiti Kebangsaan Malaysia 2025-03 Article PeerReviewed application/pdf en http://journalarticle.ukm.my/25772/1/113-132%20-.pdf Hamida Ali, and Norazak Senu, (2025) Direct solution of third-order linear integro-differential equation using Cubic B-Spline Method. Journal of Quality Measurement and Analysis, 21 (1). pp. 113-132. ISSN 2600-8602 https://www.ukm.my/jqma/ |
| spellingShingle | Hamida Ali, Norazak Senu, Direct solution of third-order linear integro-differential equation using Cubic B-Spline Method |
| title | Direct solution of third-order linear integro-differential equation using Cubic B-Spline Method |
| title_full | Direct solution of third-order linear integro-differential equation using Cubic B-Spline Method |
| title_fullStr | Direct solution of third-order linear integro-differential equation using Cubic B-Spline Method |
| title_full_unstemmed | Direct solution of third-order linear integro-differential equation using Cubic B-Spline Method |
| title_short | Direct solution of third-order linear integro-differential equation using Cubic B-Spline Method |
| title_sort | direct solution of third-order linear integro-differential equation using cubic b-spline method |
| url | http://journalarticle.ukm.my/25772/ http://journalarticle.ukm.my/25772/ http://journalarticle.ukm.my/25772/1/113-132%20-.pdf |