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计算一阶导数的四阶中心差分格式

计算⼀阶导数的四阶中⼼差分格式

国际经济合作

原理：利⽤指定点周围的四个点构造拉格朗⽇插值曲线：

y t (y ,y ,y ,y )t −2t −1t +2t +2y (x )=y t −2(x −x )(x −x )(x −x )

t −2t −1t −2t +1t −2t +2(x −x )(x −x )(x −x )

t −1t +1t +2+y t −1(x −x )(x −x )(x −x )

国电物资商务网t −1t −2t −1t +1t −1t +2(x −x )(x −x )(x −x )

t −2t +1t +2+y t +1(x −x )(x −x )(x −x )

t +1t −2t +1t −1t +1t +2(x −x )(x −x )(x −x )

t −2t −1t +2+y t +2(x −x )(x −x )(x −x )

t +2t −2t +2t −1t +2t +1(x −x )(x −x )(x −x )

t −2t −1t +1

分母是可以直接写出来的，记为⾃变量间隔：

h ≡x −t x t −1y (x )==y t −2

(−h )(−3h )(−4h )(x −x )(x −x )(x −x )

t −1t +1t +2+y t −1

轨道根数(h )(−2h )(−3h )(x −x )(x −x )(x −x )

t −2t +1t +2+y t +1

(3h )(2h )(−h )(x −x )(x −x )(x −x )

t −2t −1t +2+y t +2公安机关办理刑事案件程序规定2013

(4h )(3h )(h )(x −x )(x −x )(x −x )

t −2t −1t +1[−y (x −x )(x −x )(x −x )

t −2t −1t +1t +2+2y (x −x )(x −x )(x −x )

关怀的人生t −1t −2t +1t +2−2y (x −x )(x −x )(x −x )t +1t −2t −1t +2+y (x −x )(x −x )(x −x )]t +2t −2t −1t +112h 3

接下来就是求该三次函数在处的导数所以

这就是计算⼀阶导数的四阶中⼼差分格式！x t y (x )

′t y (x )=′{−y [(x −x )(x −x )+(x −x )(x −x )+(x −x )(x −x )]

t −2t +1t +2t −1t +2t −1t +1+2y [(x −x )(x −x )+(x −x )(x −x )+(x −x )(x −x )]t −1t +1t +2t −2t +2t −2t +1−2y [(x −x )(x −x )+(x −x )(x −x )+(x −x )(x −x )]

t +1t −1t +2t −2t +2t −2t −1+y [(x −x )(x −x )+(x −x )(x −x )+(x −x )(x −x )]}t +2t −1t +1t −2t +1t −2t −112h 3

y (x )=′t =={−y [(x −x )(x −x )+(x −x )(x −x )+(x −x )(x −x )]

t −2t t +1t t +2t t −1t t +2t t −1t t +1+2y [(x −x )(x −x )+(x −x )(x −x )+(x −x )(x −x )]t −1t t +1t t +2t t −2t t +2t t −2t t +1−2y [(x −x )(x −x )+(x −x )(x −x )+(x −x )(x −x )]

t +1t t −1t t +2t t −2t t +2t t −2t t −1+y [(x −x )(x −x )+(x −x )(x −x )+(x −x )(x −x )]}t +2t t −1t t +1t t −2t t +1t t −2t t −112h 31

展璞计划

{−y [(−h )(−2h )+(h )(−2h )+(h )(−h )]

t −2+2y [(−h )(−2h )+(2h )(−2h )+(2h )(−h )]

t −1−2y [(h )(−2h )+(2h )(−2h )+(2h )(h )]

t +1+y [(h )(−h )+(2h )(−h )+(2h )(h )]}t +212h 3

(y −8y +8y −y )t −2t −1t +1t +212h

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