Fourth-order compact difference schemes for the two-dimensional nonlinear fractional mobile/immobile transport models. (15th October 2021) - Chai, Li; Liu, Yang; Li, Hong
Abstract: In this article, we develop fourth-order compact difference schemes based on the linearized generalized BDF2- θ to solve the two-dimensional nonlinear fractional mobile/immobile (M/I) transport equations. We derive theoretical results, including unconditional stability and error estimates associated with solution regularity. Finally, we provide extensive numerical examples with smooth solutions to demonstrate the effectiveness and accuracy of the schemes and develop the corrected compact difference scheme to recovery convergence results with nonsmooth solutions.