  A development and an application of the localized function method based on
the Galerkin method applying a set of Sine functions to approximate the unknown
mode fields of the localized modes propagating along the photonic crystal
fibres is proposed. A way for considerably reducing the number of integrals in
the case of symmetrical holes shapes with respect to the axes of coordinate
systems located at the centers of the holes, circular, elliptical etc., is also
presented. The method does not require an expansion of the refractive index and
thus inaccuracies of the expansion can be avoided. In the case of a circular
form of the holes all integrals are solved analytically.
