Abstract Based on exponential transformation, quadratic interpolation polynomial and Pade approximation, a new high order finite difference scheme is proposed for solving the two-dimensional (2D) time-fractional convection-dominated diffusion equation (of order α ∈ (0, 1)). The resulting scheme is of ( 3 − α ) -order accuracy in time and fourth-order accuracy in space. In order to reduce the amount of computation, the alternating direction implicit (ADI) scheme is further developed. Numerical experiments are given to demonstrate the high accuracy and robustness of our new scheme.

中文翻译：

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时间分数阶对流扩散方程的一种新的高阶ADI数值差分公式

摘要 基于指数变换、二次插值多项式和Pade逼近，提出一种新的高阶有限差分格式来求解二维（2D）时间分数阶对流主导的扩散方程（α ∈ (0, 1)阶） . 得到的方案在时间上具有 ( 3 − α ) 阶精度，在空间上具有四阶精度。为了减少计算量，进一步开发了交替方向隐式（ADI）方案。给出了数值实验来证明我们新方案的高精度和鲁棒性。