一维常系数对流方程的步长定律和固有差分格式

The Step Law and Natural Difference Scheme for the One-dimensional Advection Equation with Constant Coefficients

由常用差分格式得出的差分余项中的奇数次幂项和偶数次幂项分别会产生弥散(色散或频散)和耗散效应。但是利用泰勒展开式并且使差分余项为零,可以得出一维常系数对流方程的步长定律和固有差分格式,结论也适用于解类似的变系数双曲型方程和拟线性双曲型方程。

The odd and even powers of truncation remainders of the difference schemes in common use produced respectively the dispersion and dissipation effects,but by using the Taylor series expansions and the vanished remainder,the step law and natural difference scheme for the one-dimensional advection equation with constant coefficients are presented,which also applied to solve the similar hyperbolic equation with variable coefficients and quasilinear hyperbolic equations.