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Least squares support vector regression for differential equations on unbounded domains

Author

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  • Pakniyat, A.
  • Parand, K.
  • Jani, M.

Abstract

In this paper, a numerical method based on the least-squares support vector regression, and spectral methods are developed for solving differential equations on unbounded domains. In the proposed method, Hermite functions are used as the orthogonal kernel of the support vector regression. The resulting optimization problem is then reduced to a linear system in both collocation and Galerkin approaches of the method. The systems are then analyzed, along with a discussion of the sparsity of the involving matrices. Providing some numerical examples, including fractional differential equations, the accuracy and efficiency of the method are illustrated and compared with some existing methods.

Suggested Citation

  • Pakniyat, A. & Parand, K. & Jani, M., 2021. "Least squares support vector regression for differential equations on unbounded domains," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    • Handle: RePEc:eee:chsofr:v:151:y:2021:i:c:s0960077921005865
    DOI: 10.1016/j.chaos.2021.111232
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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.
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    Cited by:

    1. Abbaszadeh, Mostafa & Zaky, Mahmoud A. & Hendy, Ahmed S. & Dehghan, Mehdi, 2024. "Supervised learning and meshless methods for two-dimensional fractional PDEs on irregular domains," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 216(C), pages 77-103.
    2. Ahadian, P. & Parand, K., 2022. "Support vector regression for the temperature-stimulated drug release," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).

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