这是一份GLA格拉斯哥大学MATHS4072_1作业代写的成功案例

$$
\rho\left(J_{p}\right)<\frac{p-1-s}{p-2}
$$
then the regions of convergence of the SOR method $\left(\rho\left(\mathscr{L}{\omega}\right)<1\right)$ are For $s=1, \quad \omega \in\left(0, \frac{p}{p-1}\right)$ and for $s=-1, \omega \in\left(\frac{p-2}{p-1}, \frac{2}{1+\rho\left(J{p}\right)}\right)$.

MATHS4072_1 COURSE NOTES ：

$$
\begin{aligned}
&\dot{x}^{k}(t)=G\left(t, x^{k}(t), x^{k-1}(t)\right), t \in[0, T], \
&x^{k}(0)=x_{0}
\end{aligned}
$$
for $k=1,2, \ldots .$ Here, the function $x^{k-1}$ is known and $x^{k}$ is to be determined.
Note that the familiar Picard iteration
$$
\begin{aligned}
&\dot{x}^{k}(t)=F\left(t, x^{k-1}(t)\right), t \in[0, T], \
&x^{k}(0)=x_{0}
\end{aligned}
$$