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We consider new implicit-explicit (IMEX) Runge-Kutta methods for hyperbolic systems of conservation laws with stiff relaxation terms.
G. Strang, On the construction and comparison of difference schemes
1968
Earlier work this paper cites.
G. B. Whitham, Linear and nonlinear waves
1974
Earlier work this paper cites.
E. Hofer A partially implicit method for large stiff systems of Ode’s with only few equations introducing small time-constants
1976
Earlier work this paper cites.
G.A. Sod, A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws
1978
Earlier work this paper cites.
E. Hairer, Order conditions for numerical methods for Partitioned ordinary differential equations
1981
Earlier work this paper cites.
K. Dekker, J. G. Verwer, Stability of Runge-Kutta Methods for Stiff Nonlinear Differential Equations
1984
Earlier work this paper cites.
J. Jenkins, M. Richman, Grad’s 13-moment system for a dense gas of inelastic spheres
1985
Earlier work this paper cites.
J. Butcher, The numerical analysis of Ordinary differential equations. Runge-Kutta and general linear methods
1987
Earlier work this paper cites.
E. Hairer, S. P. Nørsett, G. Wanner, Solving ordinary differential equations, Vol.1 Nonstiff problems
1987
Earlier work this paper cites.
E. Hairer, G. Wanner, Solving ordinary differential equations, Vol.2 Stiff and differential-algebraic problems
1987
Earlier work this paper cites.
T. P. Liu, Hyperbolic conservation laws with relaxation
1987
Earlier work this paper cites.
C. -W. Shu, Total variation diminishing time discretizations
1988
Earlier work this paper cites.
Chi-Wang Shu, S. Osher, Efficient implementation of essentially nonoscillatory shock-capturing schemes
1988
Earlier work this paper cites.
R. J. LeVeque, Numerical Methods for Conservation Laws
1992
Earlier work this paper cites.
G. Q. Chen, D. Levermore, T. P. Liu, Hyperbolic conservations laws with stiff relaxation terms and entropy
1994
Earlier work this paper cites.
U. Ascher, S. Ruuth, B. Wetton, Implicit-explicit methods for time dependent PDE’s
1995
Earlier work this paper cites.
B. O. Dia, M. Schatzman, Estimation sur la formule de Strang
1995
Cited alongside, same era.
S. Jin, Runge-Kutta methods for hyperbolic systems with stiff relaxation terms
1995
Cited alongside, same era.
S. Jin, Z.P. Xin, The relaxation schemes for systems of conservation laws in arbitrary space dimensions
1995
Cited alongside, same era.
M. Cecchi Morandi, M. Redivo-Zaglia, G. Russo, Extrapolation methods for hyperbolic systems with relaxation
1996
Cited alongside, same era.
B. O. Dia, M. Schatzman, Commutateur de certains semi-groupes holomorphes et applications aux directions alternées
1996
Cited alongside, same era.
S. Jin, C. D. Levermore, Numerical Schemes for hyperbolic conservation laws with stiff relaxation terms
A. Aw, M. Rascle, Resurrection of second order models of traffic flow ?
2000
Later among the works it cites.
T. Jahnke, C. Lubich, Error bounds for exponential operator splitting
2000
Later among the works it cites.
S. F. Liotta, V. Romano, G. Russo, Central schemes for balance laws of relaxation type
2000
Later among the works it cites.
L. Pareschi, G. Russo, Implicit-explicit Runge-Kutta schemes for stiff systems of differential equations
2000
Later among the works it cites.
C. -W. Shu, Essentially Non Oscillatory and Weighted Essentially NOn OScillatory Schemes for Hyperbolic Conservation Laws
2000
Later among the works it cites.
S. Gottlieb, C. -W. Shu, E. Tadmor, Strong-stability-preserving high order time discretization methods
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1996
Cited alongside, same era.
X. Zhong, Additive Semi-Implicit Runge-Kutta methods for computing high speed nonequilibrium reactive flows
1996
Cited alongside, same era.
U. Ascher, S. Ruuth, R. J. Spiteri, Implicit-explicit Runge-Kutta methods for time dependent Partial Differential Equations
1997
Cited alongside, same era.
R. E. Caflisch, S. Jin, G. Russo, Uniformly accurate schemes for hyperbolic systems with relaxation
1997
Cited alongside, same era.
J. Frank, W. H. Hundsdorfer, J. G. Verwer, On the stability of implicit-explicit linear multistep methods
1997
Cited alongside, same era.
M. Arora, P.L. Roe, Issues and strategies for hyperbolic problems with stiff source terms
1998
Cited alongside, same era.
U. Ascher,, L. Petzold, Computer Methods for Ordinary Differential Equations, and Differential Algebraic Equations
1998
Cited alongside, same era.
2001
Later among the works it cites.
L. Pareschi, Central differencing based numerical schemes for hyperbolic conservation laws with stiff relaxation terms
2001
Later among the works it cites.
A. Aw, A. Klar, T. Materne, M. Rascle, Derivation of continuum traffic flow models from microscopic follow the leader models
2002
Later among the works it cites.
Jianxian Qiu, Chi-Wang Shu, On the construction, comparison, and local characteristic decomposition for high-order central WENO schemes
2002
Later among the works it cites.
R. J. Spiteri, S. J. Ruuth, A new class of optimal strong-stability-preserving time discretization methods
2002
Later among the works it cites.
C. A. Kennedy, M. H. Carpenter, Additive Runge-Kutta schemes for convection-diffusion-reaction equations
2003
Later among the works it cites.
L. Pareschi, G. Russo, High order asymptotically strong-stability-preserving methods for hyperbolic systems with stiff relaxation
2003
Later among the works it cites.
M. Briani, R. Natalini, G. Russo, Implicit–Explicit numerical schemes for jump diffusion processes
2004
Later among the works it cites.
A. Marquina, S. Serna, Capturing shock waves in inelastic granular gases
2004
Later among the works it cites.
L. Pareschi, G. Russo, Stability analysis of Implicit-Explicit Runge-Kutta schemes
2004
Later among the works it cites.