Numerical Method for Solving the Nonlinear Superdiffusion Equation with Functional Delay
Vladimir Pimenov,
Andrei Lekomtsev
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 prese… Show more
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