问答题
给定常微分方程初值问题
取正整数n，并记h=(b-a)／n，x
i
=a十ih，0≤i≤n．
1)分析如下求解公式的局部截断误差y
i+1
=y
i
+
[f(x
i+1
,y
i+1
)+f(x
i
,y
i
)] (A)
2)分析如下求解公式的局部截断误差y
i+1
=y
i
+
取正整数n，并记h=(b-a)／n，x
i
=a十ih，0≤i≤n．
1)分析如下求解公式的局部截断误差y
i+1
=y
i
+
[f(x
i+1
,y
i+1
)+f(x
i
,y
i
)] (A)
2)分析如下求解公式的局部截断误差y
i+1
=y
i
+
【正确答案】正确答案：1)求解公式的局部截断误差为R
1
=y(x
i+1
)-y(x
i
)-
[f(x
i+1
,y(x
i+1
))+f(x
i
,y(x
i
))]=y(x
i+1
)-y(x
i
)-
[y"(x
i+1
)+y"(x
i
)]=hy"(x
i
)+
[f(x
i+1
,y(x
i+1
))+f(x
i
,y(x
i
))]=y(x
i+1
)-y(x
i
)-
[y"(x
i+1
)+y"(x
i
)]=hy"(x
i
)+
【答案解析】