Quasilinearization and the methods of finite difference and initial values

Methods for the solution of nonlinear boundary-value problems for ordinary differential equations are discussed and classified as either finite-difference methods or initial-value methods. Within this framework, two algorithms, which are generated using the quasilinearization method, are presented and shown to be representative of these two methods. Consequently, both of the most widely used techniques for the solution of these problems can be formulated within the framework of the quasilinearization method. The computational properties of these algorithms are also discussed.