  The paper contains a thorough theoretical analysis of the SI-method, which
was firstly introduced in arXiv:1601.04272v8 and proved to be remarkably stable
and efficient when applied to some instances of stiff boundary value problems
(like the Troesch's problem). By suggesting a more general view on the
SI-method's idea and framework, we managed to obtain sufficient conditions for
the method to be applicable to a certain class of two-point boundary value
problems. The corresponding error estimates are provided. Special attention is
devoted to the exploration of the method's capabilities via a set of numerical
examples. The implementation details of the method are discussed in fair depth.
An open-source C++ implementation of the SI-method is freely available at the
public repository https://github.com/imathsoft/MathSoftDevelopment.
