Numerical Method for Solving the Nonlinear Superdiffusion Equation with Functional Delay

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

Mathematics, 2023, vol. 11, issue 18, 1-14

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.

Keywords: space-fractional diffusion equation; nonlinear superdiffusion coefficient; delay (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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