On One-Dimensional Boundary Value Problems with Explosive Coefficients and a Specific Net Basis Oriented towards their Solution

V. V. Smelov<sup>ab

a</sup> Institute of Computational Mathematics and Mathematical Geophysics (Computing Center), Siberian Branch of the Russian Academy of Sciences, Novosibirsk
^b Novosibirsk State University

Abstract: A net functional basis, based on trigonometry, is offered. This basis is oriented towards a solution of one-dimensional diffusion and diffusion-convective boundary value problems with explosive coefficients in the Cartesian, cylindrical and spherical systens of coordinates. A more general method of investigation of boundary and conjugation conditions with respect to their belonging to principal and natural conditions is proposed. An example of the search for a generalized solution to a boundary value problem by means of the net method with arbitrary net of nodes is given.

Keywords: boundary value problem, functional net basis, conjugation conditions, arbitrary net of nodes, functional, generalized solution, energy scalar product, principal and natural conditions, sweep method.

UDC: 518.12+519.34

Received: 13.01.2014