Relaxation Runge–Kutta Methods for Hamiltonian Problems
暂无分享,去创建一个
[1] Ernst Hairer,et al. Solving Ordinary Differential Equations I: Nonstiff Problems , 2009 .
[2] Hendrik Ranocha. Mimetic properties of difference operators: product and chain rules as for functions of bounded variation and entropy stability of second derivatives , 2018, BIT Numerical Mathematics.
[3] G. Quispel,et al. A new class of energy-preserving numerical integration methods , 2008 .
[4] Gregor Gassner,et al. Split form nodal discontinuous Galerkin schemes with summation-by-parts property for the compressible Euler equations , 2016, J. Comput. Phys..
[5] Joel Nothman,et al. SciPy 1.0-Fundamental Algorithms for Scientific Computing in Python , 2019, ArXiv.
[6] J. M. Sanz-Serna,et al. Numerical Hamiltonian Problems , 1994 .
[7] Jesús María Sanz-Serna,et al. An explicit finite-difference scheme with exact conservation properties , 1982 .
[8] Ernst Hairer,et al. ON ENERGY CONSERVATION OF THE SIMPLIFIED TAKAHASHI-IMADA METHOD , 2009 .
[9] J. M. Sanz-Serna,et al. A Method for the Integration in Time of Certain Partial Differential Equations , 1983 .
[10] O. Gonzalez. Time integration and discrete Hamiltonian systems , 1996 .
[11] J. Banavar,et al. Computer Simulation of Liquids , 1988 .
[12] J. Sanz-Serna,et al. Accuracy and conservation properties in numerical integration: the case of the Korteweg-de Vries equation , 1997 .
[13] B. Cano,et al. Error Growth in the Numerical Integration of Periodic Orbits, with Application to Hamiltonian and Reversible Systems , 1997 .
[14] Hendrik Ranocha,et al. General Relaxation Methods for Initial-Value Problems with Application to Multistep Schemes , 2020, Numerische Mathematik.
[15] Manuel Calvo,et al. Error growth in the numerical integration of periodic orbits , 2011, Math. Comput. Simul..
[16] Hendrik Ranocha,et al. Generalised summation-by-parts operators and variable coefficients , 2017, J. Comput. Phys..
[17] H. Lewis,et al. A comparison of symplectic and Hamilton's principle algorithms for autonomous and non-autonomous systems of ordinary differential equations , 2001 .
[18] G. J. Cooper. Stability of Runge-Kutta Methods for Trajectory Problems , 1987 .
[19] Ernst Hairer,et al. Energy behaviour of the Boris method for charged-particle dynamics , 2018, BIT Numerical Mathematics.
[20] E. Hairer,et al. Geometric Numerical Integration: Structure Preserving Algorithms for Ordinary Differential Equations , 2004 .
[21] David P. Dobkin,et al. The quickhull algorithm for convex hulls , 1996, TOMS.
[22] J. Verwer,et al. Stability of Runge-Kutta Methods for Stiff Nonlinear Differential Equations , 1984 .
[23] Manuel Calvo,et al. On the Preservation of Invariants by Explicit Runge-Kutta Methods , 2006, SIAM J. Sci. Comput..
[24] J. M. Sanz-Serna,et al. Lack of dissipativity is not symplecticness , 1995 .
[25] David I. Ketcheson,et al. Relaxation Runge-Kutta Methods: Conservation and Stability for Inner-Product Norms , 2019, SIAM J. Numer. Anal..
[26] E. Hairer,et al. Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems , 2010 .
[27] M. P. Laburta,et al. Projection methods preserving Lyapunov functions , 2010 .
[28] Mari Paz Calvo,et al. The Development of Variable-Step Symplectic Integrators, with Application to the Two-Body Problem , 1993, SIAM J. Sci. Comput..
[29] J. Dormand,et al. High order embedded Runge-Kutta formulae , 1981 .
[30] Lawrence F. Shampine,et al. An efficient Runge-Kutta (4,5) pair , 1996 .
[31] Lisandro Dalcin,et al. Relaxation Runge-Kutta Methods: Fully Discrete Explicit Entropy-Stable Schemes for the Compressible Euler and Navier-Stokes Equations , 2019, SIAM J. Sci. Comput..
[32] J. Butcher. Numerical methods for ordinary differential equations , 2003 .
[33] E. Fehlberg,et al. Low-order classical Runge-Kutta formulas with stepsize control and their application to some heat transfer problems , 1969 .
[34] S. Osher,et al. Efficient implementation of essentially non-oscillatory shock-capturing schemes,II , 1989 .
[35] Antonella Zanna,et al. Preserving algebraic invariants with Runge-Kutta methods , 2000 .
[36] G. Quispel,et al. Geometric integration using discrete gradients , 1999, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.
[37] E. Hairer. Energy-preserving variant of collocation methods 1 , 2010 .
[38] Hendrik Ranocha,et al. Energy Stability of Explicit Runge-Kutta Methods for Non-autonomous or Nonlinear Problems , 2020, SIAM J. Numer. Anal..
[39] Hendrik Ranocha,et al. On strong stability of explicit Runge–Kutta methods for nonlinear semibounded operators , 2018, IMA Journal of Numerical Analysis.