The total first boundary value problem for equation of hiperbolic type with piecewise continuous coefficients and stationary heterogeneous

Abstract

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