# 4.19

Study the behavior of our model for Hyperion for different initial conditions. Estimate the Lyapunov exponent from calculation of $\Delta\theta$, such as those shown in Figure 4.19. Examine how this exponent varies as a function of the eccentricity of the orbit.

# 5.7

Write two programs to solve the capacitor problem of Figure 5.6 and 5.7, one using the Jacobi method and one using the SOR algorithm. For a fixed accuracy (as set by the convergence test) compare the number of iterations, $N_{iter}$, that each algorithm requires as a function of the number of grid elements, $L$. Show that for the Jacobi method $N_{iter}\sim L^2$, while SOR $N_{iter}\sim L$. (非常正经的计算机算法研究方式^_^）

$$\alpha = \frac{2}{1+\pi /L}$$