其中 h h h为步长， x 0 x_0 x0为待求点。
前向差商 f ( x 0 + h ) − f ( x 0 ) h = f ′ ( x 0 ) + h 2 f ′ ′ ( x 0 ) + ⋯ \frac{f(x_0+h)-f(x_0)}{h}=f^{\prime}(x_0)+\frac h2f^{\prime\prime}(x_0)+\cdots hf(x0+h)−f(x0)=f′(x0)+2hf′′(x0)+⋯后向差商 f ( x 0 ) − f ( x 0 − h ) h = f ′ ( x 0 ) − h 2 f ′ ′ ( x 0 ) + ⋯ \frac{f(x_0)-f(x_0-h)}{h}=f^{\prime}(x_0)-\frac h2f^{\prime\prime}(x_0)+\cdots hf(x0)−f(x0−h)=f′(x0)−2hf′′(x0)+⋯中心差商 f ( x 0 + h ) − f ( x 0 − h ) 2 h = f ′ ( x 0 ) + h 2 6 f ′ ′ ′ ( x 0 ) + ⋯ \frac{f(x_0+h)-f(x_0-h)}{2h}=f^{\prime}(x_0)+\frac {h^2}6 f^{\prime\prime\prime}(x_0)+\cdots 2hf(x0+h)−f(x0−h)=f′(x0)+6h2f′′′(x0)+⋯ 等价形式： f ( x 0 + 0.5 h ) − f ( x 0 − 0.5 h ) h = f ′ ( x 0 ) + h 2 24 f ′ ′ ′ ( x 0 ) + ⋯ \frac{f(x_0+0.5h)-f(x_0-0.5h)}{h}=f^{\prime}(x_0)+\frac {h^2}{24}f^{\prime\prime\prime}(x_0)+\cdots hf(x0+0.5h)−f(x0−0.5h)=f′(x0)+24h2f′′′(x0)+⋯ 一阶双曲型方程 ( 1 ) (1) (1)的几种差分格式{ ∂ u ∂ t + a ∂ u ∂ x = 0 , − ∞ < x < + ∞ , 0 < t < T u ( x , 0 ) = φ ( x ) , − ∞ < x < + ∞ , (1) \left\{ \begin{aligned} & \frac{\partial u}{\partial t}+a\frac{\partial u}{\partial x}=0,\ -\inftyhttps://www.shan-machinery.com
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