Stability of some boundary value methods for IVPs Original Research Article

We investigate the stability properties of some classes of linear two-step methods of high order and involving derivatives of the solution, up to the order three. These methods are suitable to be used as boundary value methods (BVMs) for solving initial value problems (IVPs). The advantages with respect to other two-step BVMs are the following: (1) possibility of attaining high order of accuracy, without destroying the tridiagonality of the discretization matrix, and, (2) assurance of maintaining the accuracy of the complessive BVM of the same order as that of the basic method.