Boundary Value Problems When to Use Use this skill when working on boundary-value-problems problems in odes pdes. Decision Tree 1. Problem Classification - Two-point BVP: conditions at x=a and x=b? - Sturm-Liouville: eigenvalue problem? - Mixed conditions: Dirichlet, Neumann, Robin? 2. Shooting Method - Convert BVP to IVP - Guess missing initial conditions - Iterate to satisfy boundary conditions - + root finding 3. Finite Difference Method - Discretize domain: x i = a + i h - Replace derivatives with differences: y'' (y {i+1} - 2y i + y {i-1})/h^2 - Solve resulting linear system - 4. Colloca…