Boundary value problems

Boundary value problems are ordinary differential equations where information is known on the boundaries of the domain. E.g.:

\[\frac{d^2 f}{dt^x} +\frac{df}{dx} = 1, \quad f(x=0) = 1000, f(x=1) = 1\]

One option is to shoot a solution from one side using our IVP methods and check if it hits the other boundary, which is called the shooting method.

Alternately, we can also exploit the fact that we have information at both sides to solve a discretized representation of the solution simultaneously.