Numerical solution of non-linear fourth order fractional sub-diffusion wave equation with time delay

Abstract

In this paper, we constructed a linearized compact difference scheme for fourth order non-linear fractional sub-diffusion equation with time delay and variable coefficients. The primary purpose of our work is to use the idea of the L2−1σ formula for temporal dimension and compact linear operator for spatial dimension. The proposed method is unconditionally stable and convergent to the analytical solution with the order of convergence O(τ2+h4), where τ and h are temporal and spatial lengths, respectively. Numerical experimentation is carried out to show the efficiency and accuracy of the proposed scheme.