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

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.