Analysis of the L1 scheme for fractional wave equations with nonsmooth data

Abstract

This paper analyzes the well-known L1 scheme for fractional wave equations with nonsmooth data. A new stability estimate and temporal accuracy O(τ3−α) are obtained. In addition, a modified L1 scheme is proposed, and its stability and temporal accuracy O(τ2) are also derived under nonsmooth data. The convergence of the two schemes in the inhomogeneous case are also established. Finally, numerical experiments are performed to verify the theoretical results.