Numerical Methods for ODE BVPs

Two-point ODE boundary value problems are discussed. Discretized linear boundary value problems can be solved directly with a banded matrix solve. For discretized nonlinear boundary values problems, Newton’s method should be used to linearize the equations for the solution update, which then can be found with a banded matrix solve. As a nonlinear example, the solution to the boundary layer equation is computed and then compared with a uniform global approximation.