  Boundary value problems in ODEs arise in modelling many physical situations
from microscale to mega scale. Such two-point boundary value problems (BVPs)
are complex and often possess no analytical closed form solutions. So, one has
to rely on approximating the actual solution numerically to a desired accuracy.
To approximate the solution numerically, several numerical methods are
available in the literature. In this chapter, we explore on finding numerical
solutions of two-point BVPs arising in higher order ODEs using the shooting
technique. To solve linear BVPs, the shooting technique is derived as an
application of linear algebra. We then describe the nonlinear shooting
technique using Newton-Kantorovich theorem in dimension n>1. In the
one-dimensional case, Newton-Raphson iterates have rapid convergence. This is
not the case in higher dimensions. Nevertheless, we discuss a class of BVPs for
which the rate of convergence of the underlying Newton iterates is rapid. Some
explicit examples are discussed to demonstrate the implementation of the
present numerical scheme.
