Abstract
Two fourth-order approximations for fractional derivatives are presented. These approximations are constructed from an approximation of order 2 through convex combinations of two different shifts eliminating the third-order term and then approximating the remaining second-order term with a central difference approximation. The constructed approximations are applied in Crank- Nicolson schemes to the one-dimensional space fractional diffusion equation. Numerical tests confirm that the schemes are unconditionally stable for any choice of space discretization and converge with order 4.
Published on
31 Dec 2022.
Peer Reviewed
