We have shown the creation and implementation of ordinary differential equations algorithms of orders higher than one, provided
that the required number of initial conditions are available. See "Higher-Order Differential Equations".
However, problems originating in engineering often require the solutions of differential equations in which the data
to be satisfied are located at two different values of the independent variable x. These are
called the boundary conditions.
There are various techniques for the solution of boundary problems and we will show methods using finite differences. These
methods approximate the differential equation by finite differences at evenly spaced mesh points.