First order piecewise collocation solution of fredholm integral equation second type using SOR iteration

• Main Authors: N. S. Mohamad, Jumat Sulaiman, N. F. A. Zainal, Azali Saudi
• Format: Conference or Workshop Item
• Language: English; English
• Published: 2021
• Subjects: Q Science (General); QA Mathematics
• Online Access: https://eprints.ums.edu.my/id/eprint/30184/3/First%20order%20piecewise%20collocation%20solution%20of%20fredholm%20integral%20equation%20second%20type%20using%20SOR%20iteration-%20Abstract.pdf; https://eprints.ums.edu.my/id/eprint/30184/2/First%20Order%20Piecewise%20Collocation%20Solution%20of%20Fredholm%20Integral%20Equation%20Second%20Type%20Using%20SOR%20Iteration.pdf; https://eprints.ums.edu.my/id/eprint/30184/; https://link.springer.com/chapter/10.1007/978-981-33-4069-5_32

We evaluate the first-order approximation solution piecewise by firstorder polynomial collocation with Quadrature scheme on second-type Fredholm integral equations. This discretization derived the formulation to solve the first order piecewise approximation equation in which the linear system was built. The SOR method was described as a linear solver in which its formulation was constructed and applied in this study. In order to obtain the approximation solutions, the combination of SOR iterative method with the first-order piecewise polynomial by collocation with quadrature scheme has shown that performance of SOR method is superior than Jacobi method in terms of number of iterations and time of completion.