Open AccessОбобщенная задача Римана о распаде разрыва с дополнительными условиями на границе и ее применение для построения вычислительных алгоритмов
Author(s) -
Юрий Иванович Скалько,
Yuriy Skalko,
Сергей Юрьевич Гриднев,
Sergey Gridnev
Publication year - 2019
Publication title -
itogi nauki i tehniki. seriâ, sovremennye problemy matematiki, fundamentalʹnye napravleniâ
Language(s) - English
Resource type - Journals
ISSN - 0233-6723
DOI - 10.36535/0233-6723-2019-170-38-50
Subject(s) - mathematics , discontinuity (linguistics) , riemann problem , algebraic equation , hyperbolic partial differential equation , boundary value problem , initial value problem , mathematical analysis , constant (computer programming) , numerical partial differential equations , system of linear equations , differential equation , riemann hypothesis , nonlinear system , computer science , physics , quantum mechanics , programming language
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 an approximate solution of the generalized Riemann problem on the breakup of a discontinuity under additional conditions at the boundaries, which allows one to reduce the problem of finding the values of variables on both sides of the discontinuity surface of the initial data to the solution of a system of algebraic equations. We construct a computational algorithm for an 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; it is used for solving some applied problems associated with oil production.