Application of Hermite–Padé approximation for detecting singularities of some boundary value problems

Abstract

A computational approach to the investigation of bifurcations, based on the use of a special type of Hermite–Padé approximant, is presented. The first part of this study is a review of a singularity extraction technique based on the assumption that the given series is the local representation of an algebraic function in the independent variable. The principal merit of the procedure is its ability to reveal the underlying problem of the branches solution which are represented by the original series. In the final section, numerical results are presented for Dean flow and two problems coming from heat transfer modelling and whose solutions are obtained by means of a regular perturbation method.