Discrete transparent boundary conditions for the Schrödinger equation: fast calculation, approximation, and stability, Communications in Mathematical Sciences, vol.1, issue.3, pp.501-556, 2003. ,
Multi-dimensional hyperbolic partial differential equations, First-order systems and applications, 2006. ,
Discrete artificial boundary conditions for the linearized Korteweg-de Vries equation. Numerical Methods for Partial Differential Equations, An International Journal, vol.32, issue.5, pp.1455-1484, 2016. ,
Discrete transparent boundary conditions for the mixed KDV-BBM equation, Journal of Computational Physics, vol.345, pp.484-509, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01373388
A stiffly stable semi-discrete scheme for the characteristic linear hyperbolic relaxation with boundary, ESAIM: Mathematical Modelling and Numerical Analysis, 2020. ,
URL : https://hal.archives-ouvertes.fr/hal-02136776
, The Boltzmann Equation. Applied Mathematical Sciences, 1988.
Hyperbolic conservation laws with stiff relaxation terms and entropy, Communications on Pure and Applied Mathematics, vol.47, issue.6, pp.787-830, 1994. ,
Theoretical and Numerical Structure for Reacting Shock Waves, SIAM Journal on Scientific and Statistical Computing, vol.7, issue.4, pp.1059-1080, 1986. ,
Transparent numerical boundary conditions for evolution equations: derivation and stability analysis, Toulouse. Mathématiques. Série, vol.6, issue.2, pp.259-327, 2019. ,
URL : https://hal.archives-ouvertes.fr/hal-01369975
, On a boundary extrapolation theorem by Kreiss. Mathematics of Computation, vol.31, pp.469-477, 1977.
Exact Nonreflecting Boundary Conditions for the Time Dependent Wave Equation, SIAM Journal on Applied Mathematics, vol.55, issue.2, pp.280-297, 1995. ,
Time dependent problems and difference methods, 2013. ,
Global Existence of Smooth Solutions for Partially Dissipative Hyperbolic Systems with a Convex Entropy. Archive for Rational Mechanics and, Analysis, vol.169, issue.2, pp.89-117, 2003. ,
The relaxation schemes for systems of conservation laws in arbitrary space dimensions, Communications on Pure and Applied Mathematics, vol.48, issue.3, pp.235-276, 1995. ,
Theory and Application of the Z-Transform Method, 1964. ,
Discrete Transparent Boundary Conditions for the Linearized Green-Naghdi System of Equations, SIAM Journal on Numerical Analysis, vol.58, issue.1, pp.657-683, 2020. ,
URL : https://hal.archives-ouvertes.fr/hal-01613071
, Landau. Statistical Physics, 1980.
Hyperbolic conservation laws with relaxation, Communications in Mathematical Physics, vol.108, issue.1, pp.153-175, 1987. ,
Signals and Systems (2Nd Ed, 1996. ,
Water waves. The mathematical theory with applications, 1992. ,
Introduction to Physical Gas Dynamics, vol.70, 1966. ,
Linear and nonlinear waves, 1974. ,
Stiff Well-Posedness and Asymptotic Convergence for a Class of Linear Relaxation Systems in a Quarter Plane, Journal of Differential Equations, vol.167, issue.2, pp.388-437, 2000. ,
Boundary conditions for hyperbolic systems with stiff source terms, Indiana University Mathematics Journal, vol.48, issue.1, pp.115-137, 1999. ,
Singular Perturbations of First-Order Hyperbolic Systems with Stiff Source Terms, Journal of Differential Equations, vol.155, issue.1, pp.89-132, 1999. ,
Entropy and Global Existence for Hyperbolic Balance Laws. Archive for Rational Mechanics and, Analysis, vol.172, issue.2, pp.247-266, 2004. ,
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