A higher‐order unconditionally stable scheme for the solution of fractional diffusion equation

What is it about?

In this paper, a higher‐order compact finite difference scheme with multigrid algorithm is applied for solving one‐dimensional time fractional diffusion equation. The second‐order derivative with respect to space is approximated by higher‐order compact difference scheme. Then, Grünwald–Letnikov approximation is used for the Riemann–Liouville time derivative to get an implicit scheme. The scheme is based on a heptadiagonal matrix with eighth‐order accurate local truncation error. Fourier analysis is used to analyze the stability of higher‐order compact finite difference scheme. Matrix analysis is used to show that the scheme is convergent with the accuracy of eighth‐order in space. Numerical experiments confirm our theoretical analysis and demonstrate the performance and accuracy of our proposed scheme.

Featured Image

Why is it important?

The aim of this paper is to present the solution of fractional diffusion equation using HOC difference scheme based on compact eighth order. To the best of our knowledge, there is no such report with higher-order scheme in terms of space variable. Hence, it is of great interest to investigate the HOC finite difference method for FDEs.