Comments on the use of block methods for solving singular boundary value problems

Singular boundary-value problems appear frequently on the modellization of many physical phenomena as in catalytic diffusion reactions, chemical kinetics, thermal-explosion theory, or electro hydrodynamics, among others. The singular Lane-Endem equation is a typical kind of equation modelling some of those problems. Unfortunately, just in few occasions the exact solutions can be obtained. In this situation the block methods have been used largely for approximating different kind of differential problems. We propose its use for solving singular boundary value problems. The proposed strategy consist in a block method combined with an appropriate set of formulas which are developed at the first subinterval to circumvent the singularity at the left end of the integration interval. Some examples are presented to validate the efficiency of the proposed strategy.