Stability and Convergence of Modified Du Fort-Frankel Schemes for Solving Time-Fractional Subdiffusion Equations

A class of modified Du Fort-Frankel-type schemes is investigated for fractional subdiffusion equations in the Jumarie's modified Riemann-Liouville form with constant, variable or distributed fractional order. New explicit difference methods are constructed by combining the approximation of the modified fractional derivative with the idea of Du Fort-Frankel scheme, well-known for ordinary diffusion equations. Unconditional stability of the explicit methods is established in the sense of a discrete energy norm. The proposed schemes are shown to be convergent under the time-step (consistency) restriction of the classical Du Fort-Frankel scheme. Numerical examples are included to support our theoretical results.