Chapter 7.1, Problem 2SA

Set compressibility to the moderate value $c=0.01$ . Solve the BVP by the Shooting Method for pressures $p=0$ and 3. The function $F$ in the Shooting Method should use the three missing initial values $y_2\left(0\right)$, $y_5\left(0\right)$, $y_7\left(0\right)$ as input and the three final values $y_1\left(\pi /2\right)$, $y_2\left(\pi /2\right)$, $y_6\left(\pi /2\right)$ as output. The multivariate solver Broyden II from Chapter 2 can be used to solve for the roots of $F$ . Compare with the correct solution (7.10). Note that, for both values of $p$ . various initial conditions for Broyden’s Method all result in the same solution trajectory. How much does the radius decrease when $p$ increases from 0 to 3?