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Half-Sweep Newton-SOR Iteration with Quadrature Scheme to Solve Nonlinear Fredholm Integral Equations

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Proceedings of the 8th International Conference on Computational Science and Technology

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 835))

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Abstract

This paper aims to propose an efficient and fast iterative method to solve the nonlinear Fredholm integral equations of the second kind (NFIE-2). For this starting point, we discretize the general NFIE-2 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 Newton-Successive Overrelaxation (NSOR) method with the half-sweep (HS) complexity reduction technique to boost its convergence rate, called half-sweep  NSOR  (HSNSOR) method. Also, we used the standard form of Newton-Gauss–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 half-sweep to the existing NSOR provides us with a method that converge faster than the FSNGS and FSNSOR.

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Acknowledgements

The authors would like to acknowledge the financial support by Universiti Malaysia Sabah under UMSGreat: GUG0485-1/2020.

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Authors and Affiliations

  1. Faculty of Science and Natural Resources, Universiti Malaysia Sabah, Kota Kinabalu, 88400, Sabah, Malaysia

    L. H. Ali, J. Sulaiman & M. M. Xu

  2. Faculty of Computing and Informatics, Universiti Malaysia Sabah, Kota Kinabalu, 88400, Sabah, Malaysia

    A. Saudi

  3. School of Mathematics and Information Technology, Xingtai University, 054000, Xingtai, Hebei, P. R. China

    M. M. Xu

Authors
  1. L. H. Ali
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  2. J. Sulaiman
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  3. A. Saudi
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  4. M. M. Xu
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Editor information

Editors and Affiliations

  1. Faculty of Computing and Informatics, Universiti Malaysia Sabah, Kota Kinabalu, Malaysia

    Rayner Alfred

  2. School of Information, Science, Security, Network, Japan Advanced Institute of Science and Technology, Ishikawa, Japan

    Yuto Lim

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Ali, L.H., Sulaiman, J., Saudi, A., Xu, M.M. (2022). Half-Sweep Newton-SOR Iteration with Quadrature Scheme to Solve Nonlinear Fredholm Integral Equations. In: Alfred, R., Lim, Y. (eds) Proceedings of the 8th International Conference on Computational Science and Technology. Lecture Notes in Electrical Engineering, vol 835. Springer, Singapore. https://doi.org/10.1007/978-981-16-8515-6_53

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