text: Comments on the use of block methods for solving singular boundary value problems | ITM Web of Conferences
  All issues Volume 34 (2020) ITM Web Conf., 34 (2020) 01005 Abstract
  https://doi.org/10.1051/itmconf/20203401005
  Higinio Ramos1,2,3*
  1 Departamento de Matemática Aplicada, Universidad de Salamanca Casas del Parque sn., 37008 Salamanca (Spain).
  2 Escuela Politécnica Superior de Zamora Avda. Requejo, 33, 49022 Zamora (Spain).
  3 Scientific Computing Group, Universidad de Salamanca, Facultad de Ciencias 37008 Salamanca (Spain).
  * e-mail: higra@usal.es
  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.
  ITM Web of Conferences 34, 02011 (2020)
  On the Ψ-asymptotic equivalence of the Ψ-bounded solutions of two Lyapunov matrix differential equations