Some Aspects of the Numerical Solution of Two-Point Boundary Value Problem by the Method of Orthogonal Transferring of the Boundary Conditions

Abstract
The two-point boundary value problem is traditionally used in continuum mechanics for describing heat and mass transfer, oscillatory processes, electrical properties and other phenomena that depend on the boundary conditions. These mathematical models are of great practical importance in the study of the physical properties and structure of the mesogenic liquid crystals.Some approaches to the implementation of one of numerical methods for solving the two-point boundary value problem by the two Cauchy problems are discussed. Methods for solving these problems and the problems of linear algebra are chosen. This method has some advantages over the difference schemes in continuum mechanics problems.

Keywords: two-point boundary value problem, Cauchy problem, system of ordinary differential equations, system of linear algebraic equations, numerical methods