Stable Difference Schemes for Fractional Parabolic PDE

Abstract

The stable difference schemes for the multidimensional fractional parabolic equation with Dirichlet and Neumann boundary conditions are presented. Stability estimates and almost coercive stability estimates with ln 1/tau vertical bar vertical bar h vertical bar 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.