Abstract:
In this paper, we construct an approximation of the fundamental solution of a problem for a hyperbolic system of first-order linear differential equations with constant coefficients.
We propose an algorithm for the approximate solution of the generalized Riemann problem on the discontinuity of a decay under additional conditions on the boundaries.
This algorithm reduces the problem of finding values of variables on both sides of the discontinuity surface of the initial data to solving a system of algebraic equations whose right-hand sides depend on the values of the variables at the initial moment of time at a finite number of points.
Based on these solutions, we develop a computational algorithm for the approximate solution of the initial-boundary-value problem for a hyperbolic system of first-order linear differential equations. The algorithm is implemented for a system of equations of elastic dynamics; moreover, we use it to solve some applied problems related to oil production.
Keywords:decay of a discontinuity, conjugation conditions, hyperbolic system, generalized function, Cauchy problem, matrix Green function, characteristic, Riemann invariant, equations of elastic dynamics.