A novel finite difference discrete scheme for the time fractional diffusion-wave equation

In this article, we consider initial and boundary value problems for the diffusion-wave equation involving a Caputo fractional derivative (of order α, with 1<α<2) in time. A novel finite difference discrete scheme is developed for using discrete fractional derivative at time tn in which some new coefficients (k+12)2−α−(k−12)2−α instead of (k+1)2−α−k2−α are derived. Stability and convergence of the method are rigorously established. We prove that the novel discretization is unconditionally stable, and the optimal convergence orders O(τ3−α+h2) both in L2 and L∞ are derived, where τ is the time step and h is space mesh size. Moreover, the applicability and accuracy of the scheme are demonstrated by numerical experiments to support our theoretical analysis.