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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. 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.
    4. 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.
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    7. 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.
    8. Chesney, Marc & Scott, Louis, 1989. "Pricing European Currency Options: A Comparison of the Modified Black-Scholes Model and a Random Variance Model," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 24(3), pages 267-284, September.
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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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