Abstract:
A new implicit difference approximation to solve a time fractional derivative equation is proposed.The spatial derivative is directly discretized by central difference scheme. To approximate the Caputo fractional derivative, it is established by means of the quadratic interpolation approximation. Using three points u(x,tn-2),u(x,tn-1),u(x,tn) for the integrand u(x,t) on each small interval \[tn-1,tn\](2≤n≤N), while the linear interpolation approximation is applied on the first small interval \[t0,t1\].Using the energy norm, the unconditional stability and convergence of the scheme are proved.Finally, a numerical experiment shows that the scheme is efficient.
