Spectral method for the fractional diffusion-wave equation with variable coefficients

摘要

In this paper, we consider the spectral method for the time fractional diffusion-wave equation with variable coefficients in a bounded domain. The time fractional derivative is described in the Caputo sense with the order γ (1 ≤ γ ≤ 2). We transform the equation into an equivalent form with Riemann-Liouville fractional integral operator, based on the weighted and shifted Gru?nwald difference operator, the convergence rate of the fully discrete scheme in L norm is O(τ + N). Detailed analysis for the stability and convergence of the fully discrete scheme is given. Numerical examples are presented to demonstrate the theoretical results.