High-Order Asymptotic-Preserving Methods for Fully Nonlinear Relaxation Problems
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[1] Gabriella Puppo,et al. High-Order Relaxation Schemes for Nonlinear Degenerate Diffusion Problems , 2006, SIAM J. Numer. Anal..
[2] Luc Mieussens,et al. A New Asymptotic Preserving Scheme Based on Micro-Macro Formulation for Linear Kinetic Equations in the Diffusion Limit , 2008, SIAM J. Sci. Comput..
[3] Lorenzo Pareschi,et al. Numerical Schemes for Hyperbolic Systems of Conservation Laws with Stiff Diffusive Relaxation , 2000, SIAM J. Numer. Anal..
[4] Ernst Hairer,et al. Solving Ordinary Differential Equations I: Nonstiff Problems , 2009 .
[5] Stéphane Cordier,et al. An asymptotic preserving scheme for hydrodynamics radiative transfer models , 2007, Numerische Mathematik.
[6] G. Russo,et al. Implicit-explicit runge-kutta schemes and applications to hyperbolic systems with relaxation , 2005 .
[7] E. Hairer,et al. Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems , 2010 .
[8] Xiaolin Zhong,et al. Additive Semi-Implicit Runge-Kutta Methods for Computing High-Speed Nonequilibrium Reactive Flows , 1996 .
[9] Lorenzo Pareschi,et al. Implicit-Explicit Runge-Kutta Schemes for Hyperbolic Systems and Kinetic Equations in the Diffusion Limit , 2013, SIAM J. Sci. Comput..
[10] Lorenzo Pareschi,et al. Diffusive Relaxation Schemes for Multiscale Discrete-Velocity Kinetic Equations , 1998 .
[11] P. Hartman. Ordinary Differential Equations , 1965 .
[12] Philippe G. LeFloch,et al. Late-time/stiff-relaxation asymptotic-preserving approximations of hyperbolic equations , 2010, Math. Comput..
[13] Giovanni Russo,et al. On a Class of Uniformly Accurate IMEX Runge--Kutta Schemes and Applications to Hyperbolic Systems with Relaxation , 2009, SIAM J. Sci. Comput..
[14] Giovanni Samaey,et al. Asymptotic-preserving Projective Integration Schemes for Kinetic Equations in the Diffusion Limit , 2010, SIAM J. Sci. Comput..
[15] Lorenzo Pareschi,et al. Implicit-explicit runge-kutta schemes and applications to hyperbolic systems with relaxation , 2010, 1009.2757.
[16] Philippe G. LeFloch,et al. Late-time relaxation limits of nonlinear hyperbolic systems. A general framework , 2010 .
[17] Bruno Després,et al. Asymptotic preserving and positive schemes for radiation hydrodynamics , 2006, J. Comput. Phys..
[18] Chi-Wang Shu. Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws , 1998 .
[19] C. D. Levermore,et al. Numerical Schemes for Hyperbolic Conservation Laws with Stiff Relaxation Terms , 1996 .
[20] T. Hou,et al. Why nonconservative schemes converge to wrong solutions: error analysis , 1994 .
[21] M. Carpenter,et al. Additive Runge-Kutta Schemes for Convection-Diffusion-Reaction Equations , 2003 .
[22] A. Klar. An Asymptotic-Induced Scheme for Nonstationary Transport Equations in the Diffusive Limit , 1998 .
[23] Lorenzo Pareschi,et al. Discretization of the Multiscale Semiconductor Boltzmann Equation by Diffusive Relaxation Schemes , 2000 .
[24] Sebastiano Boscarino,et al. On an accurate third order implicit-explicit Runge--Kutta method for stiff problems , 2009 .
[25] Giovanni Russo,et al. Flux-Explicit IMEX Runge-Kutta Schemes for Hyperbolic to Parabolic Relaxation Problems , 2013, SIAM J. Numer. Anal..
[26] E. Hairer,et al. Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems , 2010 .
[27] Steven J. Ruuth,et al. Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations , 1997 .
[28] P. LeFloch. A Framework for Late-Time/Stiff Relaxation Asymptotics , 2011, 1105.1415.
[29] SEBASTIANO BOSCARINO. Error Analysis of IMEX Runge-Kutta Methods Derived from Differential-Algebraic Systems , 2007, SIAM J. Numer. Anal..
[30] L. Chambers. Linear and Nonlinear Waves , 2000, The Mathematical Gazette.