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A novel approach for solving linear Fredholm integro-differential equations via LS-SVM algorithm

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  • Sun, Hongli
  • Lu, Yanfei

Abstract

In this paper, an innovative numerical methodology is introduced for solving multiple types of linear one-dimensional Fredholm integro-differential equations using least squares support vector machine (LS-SVM) algorithm, even in singular cases. The proposed method combines the original LS-SVM model with the composite Simpson method, which transforms the original solution problem into an optimization problem with equality constraints. Then the original problem is reduced to seeking the LS-SVM model parameters, which further reduces the calculation cost. An explicit expression for the numerical solution of the Fredholm integro-differential equations is given. Finally, the constructed LS-SVM model is evaluated through numerical experiments, and the obtained solutions demonstrate the robustness and validity of the constructed model.

Suggested Citation

  • Sun, Hongli & Lu, Yanfei, 2024. "A novel approach for solving linear Fredholm integro-differential equations via LS-SVM algorithm," Applied Mathematics and Computation, Elsevier, vol. 470(C).
    • Handle: RePEc:eee:apmaco:v:470:y:2024:i:c:s0096300324000298
    DOI: 10.1016/j.amc.2024.128557
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    References listed on IDEAS

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    1. Parand, K. & Aghaei, A.A. & Jani, M. & Ghodsi, A., 2021. "A new approach to the numerical solution of Fredholm integral equations using least squares-support vector regression," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 180(C), pages 114-128.
    2. Mirzaee, Farshid & Hoseini, Seyede Fatemeh, 2017. "A new collocation approach for solving systems of high-order linear Volterra integro-differential equations with variable coefficients," Applied Mathematics and Computation, Elsevier, vol. 311(C), pages 272-282.
    3. Yifei Yang & Minjia Tan & Yuewei Dai, 2017. "An improved CS-LSSVM algorithm-based fault pattern recognition of ship power equipments," PLOS ONE, Public Library of Science, vol. 12(2), pages 1-10, February.
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