An α-robust second-order accurate scheme for a subdiffusion equation
CoRR(2024)
摘要
We investigate a second-order accurate time-stepping scheme for solving a
time-fractional diffusion equation with a Caputo derivative of order α∈ (0,1). The basic idea of our scheme is based on local integration followed
by linear interpolation. It reduces to the standard Crank–Nicolson scheme in
the classical diffusion case, that is, as α→ 1. Using a novel
approach, we show that the proposed scheme is α-robust and second-order
accurate in the L^2(L^2)-norm, assuming a suitable time-graded mesh. For
completeness, we use the Galerkin finite element method for the spatial
discretization and discuss the error analysis under reasonable regularity
assumptions on the given data. Some numerical results are presented at the end.
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