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Numerical Method for Solving the Nonlinear Superdiffusion Equation with Functional Delay

Author

Listed:
  • Vladimir Pimenov

    (Department of Computational Mathematics and Computer Science, Ural Federal University, 19 Mira Str., Yekaterinburg 620002, Russia
    N.N. Krasovskii Institute of Mathematics and Mechanics UB RAS, 16 S.Kovalevskaya Str., Yekaterinburg 620108, Russia)

  • Andrei Lekomtsev

    (Department of Computational Mathematics and Computer Science, Ural Federal University, 19 Mira Str., Yekaterinburg 620002, Russia)

Abstract

For a space-fractional diffusion equation with a nonlinear superdiffusion coefficient and with the presence of a delay effect, the grid numerical method is constructed. Interpolation and extrapolation procedures are used to account for the functional delay. At each time step, the algorithm reduces to solving a linear system with a main matrix that has diagonal dominance. The convergence of the method in the maximum norm is proved. The results of numerical experiments with constant and variable delays are presented.

Suggested Citation

  • Vladimir Pimenov & Andrei Lekomtsev, 2023. "Numerical Method for Solving the Nonlinear Superdiffusion Equation with Functional Delay," Mathematics, MDPI, vol. 11(18), pages 1-14, September.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:18:p:3941-:d:1241448
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    References listed on IDEAS

    as
    1. Lekomtsev, Andrey & Pimenov, Vladimir, 2015. "Convergence of the scheme with weights for the numerical solution of a heat conduction equation with delay for the case of variable coefficient of heat conductivity," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 83-93.
    2. Meshari Alesemi & Naveed Iqbal & Ahmed A. Hamoud & C. Rajivganthi, 2022. "The Analysis of Fractional-Order Proportional Delay Physical Models via a Novel Transform," Complexity, Hindawi, vol. 2022, pages 1-13, February.
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