On the relations between B2V Ms and Runge-Kutta collocation methods

The principal aim of this paper is a rigorous analysis of the relations between Block Boundary Value Methods (B₂V Ms) with minimal blocksize defined over a suitable nonuniform finer mesh and well-known Runge-Kutta collocation methods. Moreover, a further aspect that will be briefly investigated is the construction of an extended finer mesh for building B₂V Ms with nonminimal blocksize. Some advantages that may arise from the use of the so-obtained methods will be also discussed.