Comparative numerical laboratory
BVP Methods: Shooting versus Finite Differences — Chapter 11
Solve \(-y''=1,\ y(0)=y(1)=0\) and compare the ideas.
\[
y(x)=\frac{x(1-x)}{2}.
\]
Methods compared
| Method | Convenience | Inconvenience / warning |
|---|---|---|
| Shooting | Uses IVP technology and is intuitive. | Can be sensitive or unstable for difficult BVPs. |
| Finite differences | Directly imposes boundary values. | Requires solving algebraic systems. |
| Exact solution | Useful benchmark here. | Usually unavailable. |
Illustrative plot / animation
Numerical diagnostics
What the student must compare
- boundary residual
- profile comparison
- mesh refinement
- sensitivity to slope