Some temporal second order difference schemes for fractional wave equations

Abstract

In this article, motivated by Alikhanov's new work (Alikhanov, J Comput Phys 280 (2015), 424-438), some difference schemes are proposed for both one-dimensional and two-dimensional time-fractional wave equations. The obtained schemes can achieve second-order numerical accuracy both in time and in space. The unconditional convergence and stability of these schemes in the discrete H1-norm are proved by the discrete energy method. The spatial compact difference schemes with the results on the convergence and stability are also presented. In addition, the three-dimensional problem is briefly mentioned. Numerical examples illustrate the efficiency of the proposed schemes.