Efficient finite differences for parameter-dependent singularities in two-point boundary value problems

Abstract

We will consider the implementation of finite differences to the numerical computation of simple turning points, cubic turning points, simple bifurcation points and bifurcation points with corank 2 in B.V.Ps for ordinary differential equations. The singularity will be characterized by an equation or a set of equations which will be augmented with the original system to produce a regular problem. Block elimination will be employed for saving on the amount of work while Richardson extrapolation will be used to produce accurate results. Numerical examples will be presented to show the efficiency of the above-described algorithm.