A new Nystrom method for solving boundary value problems on the real axis

The aim of this paper is to improve an existing Nyström type method to solve Fredholm integral equations of the second kind arising from the reformulation of Boundary Value Problems (BVPs) of the second order defined on R [1]. The numerical method here considered is based on a truncated interpolation process done at the Hermite zeros, without any additional point. Its stability and convergence as well as the well conditioning of the involved linear systems are proved in the space of the bounded functions on R, under less restrictive assumptions on the functions defining the problem. Numerical examples confirming the theoretical error estimates as well as comparisons with the previous method and the method proposed in [2] are also provided.