A Numerical Method for the Variable-Order Time-Fractional Wave Equations Based on the H2N2 Approximation

Abstract

Aiming at the initial boundary value problem of variable-order time-fractional wave equations in one-dimensional space, a numerical method using second-order central difference in space and H2N2 approximation in time is proposed. A finite difference scheme with second-order accuracy in space and $3-{\gamma }^{\ast }$ order accuracy in time is obtained. The stability and convergence of the scheme are further discussed by using the discrete energy analysis method. A numerical example shows the effectiveness of the results.