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
   • scipy.integrate.solve_ivp + root finding