For the all-at-once linear system derived from the second order diagonal Runge-Kutta discrete two-dimensional heat equation,an efficient α circulant preconditioner is proposed in this paper,and the A stability of the second order diagonal Runge-Kutta method is proved.Besides,the fast computation steps of the preconditioning matrix vector product are also given.The upper bound of the spectrum of the iterative matrix has the convergence property independent of the size of the grid.Finally,the effectiveness of the preconditioner is verified by numerical experiments.
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