Labiyana Hanif Ali and Jumat Sulaiman and Azali Saudi and Ming, Xu Ming (2022) Numerical Solution of Nonlinear Fredholm Integral Equations Using HalfSweep NewtonPKSOR Iteration. Mathematics and Statistics, 10 (4). pp. 868874. ISSN 23322071
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Abstract
This paper is concerned with producing an efficient numerical method to solve nonlinear Fredholm integral equations using HalfSweep NewtonPKSOR (HSNPKSOR) iteration. The computation of numerical methods in solving nonlinear equations usually requires immense amounts of computational complexity. By implementing a HalfSweep approach, the complexity of the calculation is tried to be reduced to produce a more efficient method. For this purpose, the steps of the solution process are discussed beginning with the derivation of nonlinear Fredholm integral equations using a quadrature scheme to get the halfsweep approximation equation. Then, the generated approximation equation is used to develop a nonlinear system. Following that, the formulation of the HSNPKSOR iterative method is constructed to solve nonlinear Fredholm integral equations. To verify the performance of the proposed method, the experimental results were compared with the FullSweep NewtonKSOR (FSNKSOR), HalfSweep NewtonKSOR (HSNKSOR), and FullSweep NewtonPKSOR (FSNPKSOR) using three parameters: number of iteration, iteration time, and maximum absolute error. Several examples are used in this study to illustrate the efficiency of the tested methods. Based on the numerical experiment, the results appear that the HSNPKSOR method is effective in solving nonlinear Fredholm integral equations mainly in terms of iteration time compared to rest tested methods.
Item Type:  Article 

Keyword:  Nonlinear Fredholm Integral Equations , NewtonPKSOR , Halfsweep NewtonPKSOR , HSNPKSOR , Iterative method , Quadrature scheme 
Subjects:  Q Science > QA Mathematics > QA1939 Mathematics > QA299.6433 Analysis 
Department:  FACULTY > Faculty of Computing and Informatics 
Depositing User:  SAFRUDIN BIN DARUN  
Date Deposited:  16 Nov 2022 09:14 
Last Modified:  16 Nov 2022 09:14 
URI:  https://eprints.ums.edu.my/id/eprint/34859 
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