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- W4211055963 abstract "In this study, we applied Newton method with a new version of KSOR, called PKSOR to form NPKSOR in solving nonlinear second kind Fredholm integral equations. A new version of KSOR is an update to the KSOR method with two relaxation parameters. The properties of KSOR helps in enlargement of the solution domain so the relaxation parameter can take the value <img src=image/13425283_01.gif>. With PKSOR, the relaxation parameter in KSOR <img src=image/13425283_02.gif> is treated into two different relaxation paramaters as <img src=image/13425283_03.gif> and <img src=image/13425283_04.gif> which resulting lower number of iteration compared to the KSOR method. By combining the Newton method with PKSOR, we intend to from more efficient method to solve the nonlinear Fredholm integral equations. The discretization part of this study is done using first-order quadrature scheme to develop a nonlinear system. We formulate the solution of the nonlinear system using the given approach by reducing it to a linear system and then solving it using iterative methods to obtain an approximate solution. Furthermore, we compare the results of the proposed methods with NKSOR and NGS methods on three examples. Based on our findings, the NPKSOR method is more efficient than NKSOR and NGS methods. By implementing the NPKSOR method, we can boost the convergence rate of the iteration by considering two relaxation parameters, resulting in a lower number of iteration and computational time." @default.
- W4211055963 created "2022-02-13" @default.
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- W4211055963 date "2022-01-01" @default.
- W4211055963 modified "2023-09-23" @default.
- W4211055963 title "Newton-PKSOR with Quadrature Scheme in Solving Nonlinear Fredholm Integral Equations" @default.
- W4211055963 doi "https://doi.org/10.13189/ms.2022.100123" @default.
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