In this paper, an accurate O(τ3 +h2 ) method for solving the one-dimensional diffusion equation were proposed. A central finite difference approximation of second-order for discretizing spatial derivatives and a Pade [2/1] approximation method of third-order for the time integration of the resulted linear system of ordinary differential equations were applied. The proposed method has second-order accuracy in space and third-order accuracy in time variables , and the stability was discussed. Numerical experiments are compared with Crank -Nicolson scheme. Numerical experiments show that this scheme can cope with discontinuities in the boundary conditions and initial conditions is also suitable for long time interval problems.%对扩散方程提出了精度为O(τ3+h2)的差分格式,首先对空间变量中心差分格式离散,所得到常微分方程组利用指数函数的Pade[ 2/1]逼近,得到空间二阶时间三阶精度的两层绝对稳定的隐式差分格式,并讨论了稳定性.数值结果与Crank-Nicholson格式进行比较,数值结果表明,该格式不但有效地解决初始边界条件间断问题,而且适合于大时间步长问题.
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