A Compact Difference Scheme for Fourth-Order Temporal Multi-Term Fractional Wave Equations and Maximum Error Estimates

Abstract

A spatial compact difference scheme for a class of fourth-order temporal multi-term fractional wave equations is developed. The original problem is reduced to a lower order system and the corresponding time fractional derivatives are approximated by the $L$1-formula. The unconditional stability and convergence of the difference scheme are proved by the energy method. Numerical experiments support theoretical results.