A new stable splitting for singularly perturbed ODEs
暂无分享,去创建一个
[1] P. Degond,et al. All speed scheme for the low Mach number limit of the isentropic Euler equations , 2009, 0908.1929.
[2] G. Russo,et al. Implicit-explicit Runge-Kutta schemes for stiff systems of differential equations , 2000 .
[3] Shi Jin. ASYMPTOTIC PRESERVING (AP) SCHEMES FOR MULTISCALE KINETIC AND HYPERBOLIC EQUATIONS: A REVIEW , 2010 .
[4] G. Russo,et al. IMEX RUNGE-KUTTA SCHEMES FOR HYPERBOLIC SYSTEMS WITH DIFFUSIVE RELAXATION , 2012 .
[5] S. Schochet. Fast Singular Limits of Hyperbolic PDEs , 1994 .
[6] A. Bressan. Hyperbolic Systems of Conservation Laws , 1999 .
[7] Ernst Hairer,et al. The numerical solution of differential-algebraic systems by Runge-Kutta methods , 1989 .
[8] Michel Crouzeix,et al. Une méthode multipas implicite-explicite pour l'approximation des équations d'évolution paraboliques , 1980 .
[9] Chi-Wang Shu,et al. The Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. IV. The multidimensional case , 1990 .
[10] Giacomo Dimarco,et al. Asymptotic Preserving Implicit-Explicit Runge-Kutta Methods for Nonlinear Kinetic Equations , 2012, SIAM J. Numer. Anal..
[11] M. Carpenter,et al. Additive Runge-Kutta Schemes for Convection-Diffusion-Reaction Equations , 2003 .
[12] SEBASTIANO BOSCARINO. Error Analysis of IMEX Runge-Kutta Methods Derived from Differential-Algebraic Systems , 2007, SIAM J. Numer. Anal..
[13] Mária Lukácová-Medvid'ová,et al. Adaptive discontinuous evolution Galerkin method for dry atmospheric flow , 2014, J. Comput. Phys..
[14] Steven J. Ruuth,et al. Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations , 1997 .
[15] Sebastiano Boscarino,et al. On an accurate third order implicit-explicit Runge--Kutta method for stiff problems , 2009 .
[16] Jochen Schütz,et al. Flux Splitting for Stiff Equations: A Notion on Stability , 2014, J. Sci. Comput..
[17] P. Wesseling. Principles of Computational Fluid Dynamics , 2000 .
[18] E. Hairer,et al. Solving Ordinary Differential Equations I , 1987 .
[19] Pierre Degond,et al. An Asymptotic-Preserving all-speed scheme for the Euler and Navier-Stokes equations , 2011, J. Comput. Phys..
[20] A. Majda,et al. Singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit , 1981 .
[21] D. Kröner. Numerical Schemes for Conservation Laws , 1997 .
[22] Jochen Schutz. An asymptotic preserving method for linear systems of balance laws based on Galerkin's method , 2014, 1406.3940.
[23] Klaus Kaiser,et al. RS-IMEX splitting for the isentropic Euler equations , 2015 .
[24] Lorenzo Pareschi,et al. Implicit-Explicit Runge-Kutta Schemes for Hyperbolic Systems and Kinetic Equations in the Diffusion Limit , 2013, SIAM J. Sci. Comput..
[25] P. Raviart,et al. Numerical Approximation of Hyperbolic Systems of Conservation Laws , 1996, Applied Mathematical Sciences.
[26] Bernardo Cockburn,et al. The Runge-Kutta local projection P1-discontinuous-Galerkin finite element method for scalar conservation laws , 1988 .
[27] Sebastian Noelle,et al. IMEX Large Time Step Finite Volume Methods for Low Froude Number Shallow Water Flows , 2014 .
[28] T. Sonar,et al. Asymptotic adaptive methods for multi-scale problems in fluid mechanics , 2001 .
[29] Francis X. Giraldo,et al. Comparison between adaptive and uniform discontinuous Galerkin simulations in dry 2D bubble experiments , 2013, J. Comput. Phys..
[30] R. Klein. Semi-implicit extension of a Godunov-type scheme based on low Mach number asymptotics , 1995 .
[31] Jian‐Guo Liu,et al. An All-Speed Asymptotic-Preserving Method for the Isentropic Euler and Navier-Stokes Equations , 2012 .
[32] J. Anderson,et al. Fundamentals of Aerodynamics , 1984 .
[33] Uri M. Ascher,et al. Computer methods for ordinary differential equations and differential-algebraic equations , 1998 .
[34] F. Krogh,et al. Solving Ordinary Differential Equations , 2019, Programming for Computations - Python.
[35] Koottungal Revi Arun,et al. An Asymptotic Preserving all Mach Number Scheme for the Euler Equations of Gas Dynamics , 2012 .
[36] Chi-Wang Shu,et al. TVB Runge-Kutta local projection discontinuous galerkin finite element method for conservation laws. II: General framework , 1989 .
[37] R. LeVeque. Numerical methods for conservation laws , 1990 .
[38] Shi Jin,et al. Efficient Asymptotic-Preserving (AP) Schemes For Some Multiscale Kinetic Equations , 1999, SIAM J. Sci. Comput..
[39] Lorenzo Pareschi,et al. Diffusive Relaxation Schemes for Multiscale Discrete-Velocity Kinetic Equations , 1998 .
[40] Claudia Negulescu,et al. An asymptotic-preserving method for highly anisotropic elliptic equations based on a Micro-Macro decomposition , 2011, J. Comput. Phys..
[41] G. Russo,et al. High Order Asymptotically Strong-Stability-Preserving Methods for Hyperbolic Systems with Stiff Relaxation , 2003 .
[42] P. Lax. Hyperbolic systems of conservation laws , 2006 .
[43] U. Ascher,et al. Numerical Methods for Differential-Algebraic Equations , 1998 .
[44] Francis X. Giraldo,et al. Semi-Implicit Formulations of the Navier--Stokes Equations: Application to Nonhydrostatic Atmospheric Modeling , 2010, SIAM J. Sci. Comput..
[45] L. Segel,et al. Introduction to Singular Perturbations. By R. E. O'MALLEY, JR. Academic Press, 1974. $ 16.50. , 1975, Journal of Fluid Mechanics.
[46] Chi-Wang Shu,et al. TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws III: one-dimensional systems , 1989 .
[47] Willem Hundsdorfer,et al. IMEX extensions of linear multistep methods with general monotonicity and boundedness properties , 2007, J. Comput. Phys..
[48] Steven J. Ruuth,et al. Implicit-explicit methods for time-dependent partial differential equations , 1995 .
[49] Claus-Dieter Munz,et al. A Weakly Asymptotic Preserving Low Mach Number Scheme for the Euler Equations of Gas Dynamics , 2014, SIAM J. Sci. Comput..
[50] Chi-Wang Shu,et al. The Runge-Kutta local projection $P^1$-discontinuous-Galerkin finite element method for scalar conservation laws , 1988, ESAIM: Mathematical Modelling and Numerical Analysis.
[51] A. J. Gadd. A split explicit integration scheme for numerical weather prediction , 1978 .