Stability of Difference Schemes for Fractional Parabolic PDE with the Dirichlet-Neumann Conditions

Abstract

The stable difference schemes for the fractional parabolic equation with Dirichlet and Neumann boundary conditions are presented. Stability estimates and almost coercive stability estimates with ln (1/(𝜏+|ℎ|)) for the solution of these difference schemes are obtained. A procedure of modified Gauss elimination method is used for solving these difference schemes of one-dimensional fractional parabolic partial differential equations.