Three-point combined compact difference schemes for time-fractional advectiondiffusion equations with smooth solutions ?
A CCD method with the L1 formula is proposed for solving time-fractional advectiondiffusion equations. The method is globally at least fifth-order accurate in space and (2?? 2 ? ? )th-order accurate in time. The unconditional stability is proved by means of Fourier analysis. Numerical experiments are conducted to demonstrate the efficiency. The present method preserves the higher order accuracy for advection-dominated problems with the smooth solutions.
combined compact difference scheme time-fractional advectiondiffusion equations l1 formula stability convergence