Computation of singularities in B.V.P.'s using finite differences with block-elimination

Abstract

In this thesis, we will consider the numerical computation of simple turning points, simple bifurcation points and cubic turning points, for two point boundary value problems. A direct method will be employed to characterize the B.V.P.'s. Since the main block of all systems involved is the same, this will allow us to use block elimination which will reduce the work by a large factor. To obtain accurate results we will use Richardson extrapolation with small sizes. Numerical examples will also be presented.