|
Fundamental solution of an operator and its application for the approximate solution of initial-boundary-value problems
Yu. I. Skalkoa, S. Yu. Gridnevb a Moscow Institute of Physics and Technology (National Research University), Dolgoprudny, Moscow Region
b Voronezh State Technical University
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.
Citation:
Yu. I. Skalko, S. Yu. Gridnev, “Fundamental solution of an operator and its application for the approximate solution of initial-boundary-value problems”, Proceedings of the Voronezh spring mathematical school
“Modern methods of the theory of boundary-value problems. Pontryagin
readings – XXX”.
Voronezh, May 3-9, 2019. Part 4, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 193, VINITI, Moscow, 2021, 110–121
Linking options:
https://www.mathnet.ru/eng/into805 https://www.mathnet.ru/eng/into/v193/p110
|
Statistics & downloads: |
Abstract page: | 101 | Full-text PDF : | 86 | References: | 13 |
|