Abstract
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 Grunwald difference operator, the convergence rate of the fully discrete scheme in L2 norm is O(τ2 + N1−m). Detailed analysis for the stability and convergence of the fully discrete scheme is given. Numerical examples are presented to demonstrate the theoretical results.
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