Chapter 7 Ordinary differential equations - Boundary value problems

In the present chapter we develop algorithms for solving systems of (linear or nonlinear) ordinary differential equations of the boundary value type. Such equations arise in describing distributed, steady state models in one spatial dimension. The differential equations are transformed into systems of (linear and nonlinear) algebraic equations through a discretization process. In doing so, we use the tools and concepts developed in Chapter 5. In particular we will develop (i) finite differencemethods using the difference approximations given in Table 5.4, (ii) shooting methods based on methods for initial value problems seen in chapter 6 and (iii) the method of weighted residuals using notions of functional approximation developed in Chapter 5. We will conclude this chapter with an illustration of a powerful software package called COLSYS that solves a system of multi-point boundary value problems using the collocationmethod, cubic splines and adaptive mesh refinement. It is available from NETLIB.