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Distributed order Gauss-Quadrature scheme for distributed order fractional sub-diffusion model

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  • Kumar, Yashveer
  • Yadav, Poonam
  • Singh, Vineet Kumar

Abstract

In this manuscript, our goal is to design distributed order Gauss-Quadrature scheme for solving distributed order fractional sub-diffusion mathematical model based on an orthogonal generating polynomial (OGP) with respect to the weight function of distributed order anomalous time-fractional subdiffusion partial differential equation (DOT-FSPDE). Based on OGP we established a new computational algorithm for the DOT-FSPDE, which is controlled by the single input distribution weight function of DOT-FSPDE. The proposed problem has been solved numerically with the help of the OGP-Gauss quadrature rule along with an operational matrix based on the designed OGP technique. Also, we established error bounds, convergence analysis, numerical algorithms, error estimation, numerical stability and theoretical stability analysis of the designed scheme. There are several test examples which have been solved for the reliability of the proposed computational method with less CPU time. The proposed technique was found to be more accurate in comparison with the existing scheme.

Suggested Citation

  • Kumar, Yashveer & Yadav, Poonam & Singh, Vineet Kumar, 2023. "Distributed order Gauss-Quadrature scheme for distributed order fractional sub-diffusion model," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    • Handle: RePEc:eee:chsofr:v:170:y:2023:i:c:s096007792300259x
    DOI: 10.1016/j.chaos.2023.113358
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    References listed on IDEAS

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    1. Alikhanov, Anatoly A., 2015. "Numerical methods of solutions of boundary value problems for the multi-term variable-distributed order diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 12-22.
    2. Kumar, Yashveer & Singh, Vineet Kumar, 2021. "Computational approach based on wavelets for financial mathematical model governed by distributed order fractional differential equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 531-569.
    3. Singh, Somveer & Patel, Vijay Kumar & Singh, Vineet Kumar, 2018. "Application of wavelet collocation method for hyperbolic partial differential equations via matrices," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 407-424.
    4. Pourbabaee, Marzieh & Saadatmandi, Abbas, 2019. "A novel Legendre operational matrix for distributed order fractional differential equations," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 215-231.
    5. Singh, Somveer & Patel, Vijay Kumar & Singh, Vineet Kumar & Tohidi, Emran, 2017. "Numerical solution of nonlinear weakly singular partial integro-differential equation via operational matrices," Applied Mathematics and Computation, Elsevier, vol. 298(C), pages 310-321.
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    7. Pourbabaee, Marzieh & Saadatmandi, Abbas, 2022. "A new operational matrix based on Müntz–Legendre polynomials for solving distributed order fractional differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 210-235.
    8. Halil Mete Soner & Guy Barles, 1998. "Option pricing with transaction costs and a nonlinear Black-Scholes equation," Finance and Stochastics, Springer, vol. 2(4), pages 369-397.
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    Cited by:

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    2. Yang, Dongsheng & Yu, Yongguang & Wang, Hu & Ren, Guojian & Zhang, Xiaoli, 2024. "Successive lag synchronization of heterogeneous distributed-order coupled neural networks with unbounded delayed coupling," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).

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