Quadrature-piecewise collocation solutions to the fredholm integral equation of ii kind using ESOR iteration
The Fredholm integral equations (FIEs) II kind describe as the most versatile areas of study in history in which being utilized in various fields such as biology, chemistry, engineering, mathematics and physics. Thus, several numerical methods have been imposed to discretize the mentioned equations...
| Main Authors: | , , |
|---|---|
| Format: | Proceedings |
| Language: | English |
| Published: |
American Institute of Physics Inc.
2021
|
| Subjects: | |
| Online Access: | https://eprints.ums.edu.my/id/eprint/32503/1/Quadrature-piecewise%20collocation%20solutions%20to%20the%20fredholm%20integral%20equation%20of%20II%20kind%20using%20ESOR%20iteration.ABSTRACT.pdf |
| _version_ | 1825714704492789760 |
|---|---|
| author | Nor Syahida Mohamad Jumat Sulaiman Azali Saudi |
| author_facet | Nor Syahida Mohamad Jumat Sulaiman Azali Saudi |
| author_sort | Nor Syahida Mohamad |
| collection | UMS |
| description | The Fredholm integral equations (FIEs) II kind describe as the most versatile areas of study in history in which being utilized in various fields such as biology, chemistry, engineering, mathematics and physics. Thus, several numerical methods have been imposed to discretize the mentioned equations in order to get their corresponding approximation equations. In this article, the first-order piecewise polynomial collocation scheme and first-order Quadrature method have been put in order to derive the first-order quadrature-piecewise collocation approximation equation via the discretization process. The approximation equation eventually developed a dense linear system. To get the quadrature-piecewise collocation solution of this linear system, we also ascertain the performance of Extrapolated Successive Over-Relaxation (ESOR) iterative method applied to this dense linear system. Therefore, the formulation and application of iterative methods as described are also presented. Based on the numerical computational derived from the first-order quadrature-piecewise collocation approximation equation, it shows that ESOR iteration has significantly least computational efforts in terms of number of iterations and CPU time when compared with Gauss-Seidel (GS) and Successive Over-Relaxation (SOR) iterative schemes. |
| first_indexed | 2024-03-06T03:15:46Z |
| format | Proceedings |
| id | ums.eprints-32503 |
| institution | Universiti Malaysia Sabah |
| language | English |
| last_indexed | 2024-03-06T03:15:46Z |
| publishDate | 2021 |
| publisher | American Institute of Physics Inc. |
| record_format | dspace |
| spelling | ums.eprints-325032022-05-03T11:58:53Z https://eprints.ums.edu.my/id/eprint/32503/ Quadrature-piecewise collocation solutions to the fredholm integral equation of ii kind using ESOR iteration Nor Syahida Mohamad Jumat Sulaiman Azali Saudi QA299.6-433 Analysis The Fredholm integral equations (FIEs) II kind describe as the most versatile areas of study in history in which being utilized in various fields such as biology, chemistry, engineering, mathematics and physics. Thus, several numerical methods have been imposed to discretize the mentioned equations in order to get their corresponding approximation equations. In this article, the first-order piecewise polynomial collocation scheme and first-order Quadrature method have been put in order to derive the first-order quadrature-piecewise collocation approximation equation via the discretization process. The approximation equation eventually developed a dense linear system. To get the quadrature-piecewise collocation solution of this linear system, we also ascertain the performance of Extrapolated Successive Over-Relaxation (ESOR) iterative method applied to this dense linear system. Therefore, the formulation and application of iterative methods as described are also presented. Based on the numerical computational derived from the first-order quadrature-piecewise collocation approximation equation, it shows that ESOR iteration has significantly least computational efforts in terms of number of iterations and CPU time when compared with Gauss-Seidel (GS) and Successive Over-Relaxation (SOR) iterative schemes. American Institute of Physics Inc. 2021-11-18 Proceedings PeerReviewed text en https://eprints.ums.edu.my/id/eprint/32503/1/Quadrature-piecewise%20collocation%20solutions%20to%20the%20fredholm%20integral%20equation%20of%20II%20kind%20using%20ESOR%20iteration.ABSTRACT.pdf Nor Syahida Mohamad and Jumat Sulaiman and Azali Saudi (2021) Quadrature-piecewise collocation solutions to the fredholm integral equation of ii kind using ESOR iteration. https://aip.scitation.org/doi/10.1063/5.0075720 |
| spellingShingle | QA299.6-433 Analysis Nor Syahida Mohamad Jumat Sulaiman Azali Saudi Quadrature-piecewise collocation solutions to the fredholm integral equation of ii kind using ESOR iteration |
| title | Quadrature-piecewise collocation solutions to the fredholm integral equation of ii kind using ESOR iteration |
| title_full | Quadrature-piecewise collocation solutions to the fredholm integral equation of ii kind using ESOR iteration |
| title_fullStr | Quadrature-piecewise collocation solutions to the fredholm integral equation of ii kind using ESOR iteration |
| title_full_unstemmed | Quadrature-piecewise collocation solutions to the fredholm integral equation of ii kind using ESOR iteration |
| title_short | Quadrature-piecewise collocation solutions to the fredholm integral equation of ii kind using ESOR iteration |
| title_sort | quadrature piecewise collocation solutions to the fredholm integral equation of ii kind using esor iteration |
| topic | QA299.6-433 Analysis |
| url | https://eprints.ums.edu.my/id/eprint/32503/1/Quadrature-piecewise%20collocation%20solutions%20to%20the%20fredholm%20integral%20equation%20of%20II%20kind%20using%20ESOR%20iteration.ABSTRACT.pdf |
| work_keys_str_mv | AT norsyahidamohamad quadraturepiecewisecollocationsolutionstothefredholmintegralequationofiikindusingesoriteration AT jumatsulaiman quadraturepiecewisecollocationsolutionstothefredholmintegralequationofiikindusingesoriteration AT azalisaudi quadraturepiecewisecollocationsolutionstothefredholmintegralequationofiikindusingesoriteration |