【摘要】 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。更多还原

【Abstract】 Even-order accurate difference schemes of any-order derivatives can be derivedfrom the expansion of Taylor series. The formulae for calculating relevant differencecoefficients are offered here,and they are used to get some-order accurate differencecoefficients of one,two, three and four-order derivatives. The thesis also analysesthe stable conditions 0f numerical solutions of any even-order differences to acousticwave equation,and describes trial numerical mbdeling. It is shown that the higheraccuracy of difference brings less frequency dispersion and better numerical model-ing effect.更多还原