A second-order numerical method for nonlinear variable-order fractional diffusion equation with time delay.

In this paper, a linearized numerical scheme of nonlinear variable-order fractional diffusion equation with time delay is constructed. We apply the L 2 − 1 σ formula to discretize the temporal derivative and second-order central difference scheme to discretize the spatial derivative. The proposed method is unconditionally stable and convergent with O τ 2 + h 2 , where τ and h are the time and space steps, respectively. Numerical experiment demonstrates the effectiveness and accuracy of the numerical scheme. [ABSTRACT FROM AUTHOR]