Fast high-order compact difference scheme for the nonlinear distributed-order fractional Sobolev model appearing in porous media

Abstract

Listen

Translate article

In this article, we present an efficient numerical algorithm, which combines the fourth-order compact difference scheme (CDS) in space with the fast time two-mesh (TT-M) FBN-θ method, to solve the nonlinear distributed-order fractional Sobolev model appearing in porous media. We also construct the corrected CDS by adding the starting part to deal with the problem with nonsmooth solution and recovery the convergence rate. We derive optimal convergence results and prove the stability of the presented numerical algorithm. Finally, we implement numerical experiments by taking several examples with smooth and nonsmooth solutions to verify the correctness of the theoretical results, the effectiveness of the corrected algorithm and the computational efficiency of the fast algorithm.