The total first discretely-continuous boundary value problem for equation of hiperbolic type

Abstract

A new solving scheme of the general first discretely-continuous boundary value problem for a hyperbolic type equation with piecewise constant coefficients and pointed concentrations was proposed and justified. In the basis of the solving scheme is a concept of quasi-derivatives, a modern theory of systems of linear differential equations with measures, the classical Fourier method and a reduction method. The advantage of this method is a possibility to examine a problem on each breakdown segment and then to combine obtained solutions on the basis of matrix calculation. Such an approach allows to use software tools for the solution.