L. H. Ali and Jumat Sulaiman and M.M. Xu and Azali Saudi (2022) Halfsweep NewtonSOR iteration with quadrature scheme to solve nonlinear Fredholm integral equations.
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Halfsweep NewtonSOR iteration with quadrature scheme to solve nonlinear Fredholm integral equations.ABSTRACT.pdf Download (61kB) 

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HalfSweep NewtonSOR Iteration with Quadrature Scheme to Solve Nonlinear Fredholm Integral Equations.pdf Restricted to Registered users only Download (260kB)  Request a copy 
Abstract
This paper aims to propose an efficient and fast iterative method to solve the nonlinear Fredholm integral equations of the second kind (NFIE2). For this starting point, we discretize the general NFIE2 using a quadrature scheme into a corresponding nonlinear quadrature approximation equation to generate a system of nonlinear equations. Then, we convert the nonlinear system into a linear form using Newton’s method so the linear system can be solved using iterative methods. To speed up the convergence rate in solving the linear system, we proposed the hybridization of the NewtonSuccessive Overrelaxation (NSOR) method with the halfsweep (HS) complexity reduction technique to boost its convergence rate, called halfsweep NSOR (HSNSOR) method. Also, we used the standard form of NewtonGauss– Seidel and NSOR called FSNGS and FSNSOR, respectively as control methods to test the ability of this iterative method. Based on the output of numerical experiments, we found that the application of halfsweep to the existing NSOR provides us with a method that converge faster than the FSNGS and FSNSOR.
Item Type:  Proceedings 

Keyword:  Nonlinear Fredholm integral equations , Halfsweep NewtonSOR , NewtonSOR , Halfsweep approach , Quadrature scheme 
Subjects:  Q Science > QA Mathematics > QA1939 Mathematics > QA143 General 
Department:  FACULTY > Faculty of Science and Natural Resources 
Depositing User:  DG MASNIAH AHMAD  
Date Deposited:  27 Sep 2022 12:33 
Last Modified:  27 Sep 2022 12:33 
URI:  https://eprints.ums.edu.my/id/eprint/34257 
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