Some temporal second order difference schemes for fractional wave equations

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. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 970–1001, 2016