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本文从Taylor级数展开式出发，推导出了任意阶导数的任意偶数阶精度差分格式。文中给出了计算相应差分系数的公式，并计算出了一阶、二阶、三阶和四阶导数的若干阶精度差分系数。最后讨论了声波方程的任意偶数阶差分数值解的稳定性条件，并进行了数值模拟试验。结果表明差分精度越高，频散越小，数值模拟的效果越好。
In this paper, the Taylor series expansion is used to derive any even order precision difference scheme with arbitrary order derivatives. In this paper, the formulas for calculating the corresponding differential coefficients are given, and some differential resolution coefficients of first order, second order, third order and fourth order derivatives are calculated. Finally, the stability conditions of any even-order fractional solution of the acoustic wave equation are discussed and the numerical simulation is carried out. The results show that the higher the differential accuracy, the smaller the dispersion, the better the numerical simulation.