On numerical studies of multi-point boundary value problem and its fold bifurcation

Based upon shooting method, we set up a numerical method for approximating solutions and fold bifurcation solutions of second order multi-point boundary value problems. We prove the equivalence of the regularity of solutions and simple fold bifurcation solutions between the numerical method and the multi-point boundary value problems. Many numerical experiments are carried out to illustrate the theoretical analysis, from which we explore that the fold bifurcation phenomenon are generic in multi-point boundary value problems although there is no theoretical analysis in the literature so far.