Abstract
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.
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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 170, Proceedings of the Voronezh Winter Mathematical School “Modern Methods of Function Theory and Related Problems,” Voronezh, January 28 – February 2, 2019. Part 1, 2019.
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Skalko, Y.I., Gridnev, S.Y. Generalized Riemann Problem on the Decay of a Discontinuity with Additional Conditions at the Boundary and Its Application for Constructing Computational Algorithms. J Math Sci 263, 498–510 (2022). https://doi.org/10.1007/s10958-022-05945-2
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DOI: https://doi.org/10.1007/s10958-022-05945-2
Keywords and phrases
- decay of a discontinuity
- conjugation condition
- hyperbolic system
- generalized function
- Cauchy problem
- Green matrix-function
- characteristic
- Riemann invariant
- equation of elastic dynamics