Boundary value methods based on Adams-type methods Original Research Article

The aim of this paper is to derive Boundary Value Methods (BVMs) based on k-step Adams-type methods for the solution of initial value problems. BVMs lead to a discrete boundary value problem which needs one initial and k − 1 final conditions. We prove that the choice of boundary conditions, instead of the usual initial conditions, improves the stability properties of the classical Adams methods. For example, methods of order up to 6 are almost BV-A-stable, and those of order up to 9 are BV-A0-stable.