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Numerical learning approximation of time-fractional sub diffusion model on a semi-infinite domain

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  • Hajimohammadi, Zeinab
  • Parand, Kourosh

Abstract

The propose of this research is to apply a novel numerical learning approximation of time-fractional sub diffusion model on a semi-infinite domain. This model is a nonlinear fractional differential equation in two unbounded dimensions. Combination of Least Squares Support Vector Regression (LSSVR) based on generalized Laguerre Functions kernel and collocation/Galerkin method is applied to obtain the solutions. The marching in time technique is applied for time discretization. Numerical results verify that proposed methods have high convergence and performance.

Suggested Citation

  • Hajimohammadi, Zeinab & Parand, Kourosh, 2021. "Numerical learning approximation of time-fractional sub diffusion model on a semi-infinite domain," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    • Handle: RePEc:eee:chsofr:v:142:y:2021:i:c:s0960077920308274
    DOI: 10.1016/j.chaos.2020.110435
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    References listed on IDEAS

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    1. Ren, Lei & Wang, Yuan-Ming, 2017. "A fourth-order extrapolated compact difference method for time-fractional convection-reaction-diffusion equations with spatially variable coefficients," Applied Mathematics and Computation, Elsevier, vol. 312(C), pages 1-22.
    2. 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.
    3. Rad, Jamal Amani & Parand, Kourosh & Ballestra, Luca Vincenzo, 2015. "Pricing European and American options by radial basis point interpolation," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 363-377.
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    1. Hajimohammadi, Zeinab & Baharifard, Fatemeh & Ghodsi, Ali & Parand, Kourosh, 2021. "Fractional Chebyshev deep neural network (FCDNN) for solving differential models," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).

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