ABSTRACT
In this chapter, the authors develop two principal classes of numerical methods used for solving the following BVPs: The linear second-order boundary-value problem and the nonlinear second-order boundary-value problem. The finite-difference method works reasonably well for linear BVPs and does not present problems of instability. For a BVP involving a nonlinear differential equation, these methods run into problems, in that the resulting system is nonlinear. Another way of ensuring accuracy is to solve the linear system for smaller values of h and compare the solutions at the same mesh points; the round-off error, however, will eventually increase and may become large. For a BVP involving a nonlinear differential equation, these methods run into problems, in that the resulting system is nonlinear.
