Generalized Riemann Problem on the Decay of a Discontinuity with Additional Conditions at the Boundary and Its Application for Constructing Computational Algorithms

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 decay of a discontinuity under additio...

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Veröffentlicht in:Journal of mathematical sciences (New York, N.Y.) Jg. 263; H. 4; S. 498 - 510
Hauptverfasser: Skalko, Yu. I., Gridnev, S. Yu
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 09.05.2022
Springer
Springer Nature B.V
Schlagworte:
Algorithms
Boundary value problems
Cauchy problems
Decay
Differential equations
Discontinuity
Hyperbolic systems
Mathematics
Mathematics and Statistics
generalized function
35L40
35L50
35L67
35L45
characteristic
Cauchy problem
decay of a discontinuity
conjugation condition
equation of elastic dynamics
Riemann invariant
Green matrix-function
hyperbolic system
ISSN:1072-3374, 1573-8795
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Zusammenfassung: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 decay 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.
Bibliographie:ObjectType-Article-1
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ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-022-05945-2