# Implicit and implicit-explicit strong stability preserving Runge–Kutta methods with high linear order

- Published: 15 Feb 2017
- Publisher: Author(s)

[1] U. Ascher, S. Ruuth, and B. Wetton, Implicit-explicit methods for time-dependent partial differential equations, SIAM Journal on Numerical Analysis, 32 (1995), p. 797Ð823. [OpenAIRE]

[2] U. M. Ascher, S. J. Ruuth, and R. J. Spiteri, Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations, Applied Numerical Mathematics, 25 (1997), pp. 151 - 167. Special Issue on Time Integration. [OpenAIRE]

[3] S. Boscarino, L. Pareschi, and G. Russo, Implicit-explicit Runge-Kutta schemes for hyperbolic systems and kinetic equations in the diffusion limit, SIAM Journal on Scientific Computing, 35 (2013), pp. A22-A51.

[4] M. Calvo, J. de Frutos, and J. Novo, Linearly implicit runge-kutta methods for advection-reaction-diffusion equations., Applied Numerical Mathematics, 37 (2001), pp. 535- 549.

[6] [11] S. Gottlieb, D. I. Ketcheson, and C.-W. Shu, Strong Stability Preserving RungeKutta and Multistep Time Discretizations, World Scientific Press, 2011.

[26] J. F. B. M. Kraaijevanger, Contractivity of Runge-Kutta methods, BIT, 31 (1991), pp. 482-528.

[27] E. J. Kubatko, B. A. Yeager, and D. I. Ketcheson, Optimal strong-stabilitypreserving runge-kutta time discretizations for discontinuous galerkin methods, J. Sci. Comput., 60 (2014), pp. 313-344.

[28] F. Kupka, N. Happenhofer, I. Higueras, and O. Koch, Total-variation-diminishing implicit-explicit runge-kutta methods for the simulation of double-diffusive convection in astrophysics, J. Comput. Phys., 231 (2012), pp. 3561-3586.

[29] L. Pareschi and G. Russo, Implicit-explicit Runge-Kutta schemes and applications to hyperbolic systems with relaxation, Journal of Scientific Computing, 25 (2005), p. 129Ð155. [OpenAIRE]

[30] S. J. Ruuth and R. J. Spiteri, Two barriers on strong-stability-preserving time discretization methods, Journal of Scientific Computation, 17 (2002), pp. 211-220. [OpenAIRE]

[31] C.-W. Shu, Total-variation diminishing time discretizations, SIAM J. Sci. Stat. Comp., 9 (1988), pp. 1073-1084.

[32] C.-W. Shu and S. Osher, Efficient implementation of essentially non-oscillatory shockcapturing schemes, Journal of Computational Physics, 77 (1988), pp. 439-471. [OpenAIRE]

###### Related research

[1] U. Ascher, S. Ruuth, and B. Wetton, Implicit-explicit methods for time-dependent partial differential equations, SIAM Journal on Numerical Analysis, 32 (1995), p. 797Ð823. [OpenAIRE]

[2] U. M. Ascher, S. J. Ruuth, and R. J. Spiteri, Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations, Applied Numerical Mathematics, 25 (1997), pp. 151 - 167. Special Issue on Time Integration. [OpenAIRE]

[3] S. Boscarino, L. Pareschi, and G. Russo, Implicit-explicit Runge-Kutta schemes for hyperbolic systems and kinetic equations in the diffusion limit, SIAM Journal on Scientific Computing, 35 (2013), pp. A22-A51.

[4] M. Calvo, J. de Frutos, and J. Novo, Linearly implicit runge-kutta methods for advection-reaction-diffusion equations., Applied Numerical Mathematics, 37 (2001), pp. 535- 549.

[6] [11] S. Gottlieb, D. I. Ketcheson, and C.-W. Shu, Strong Stability Preserving RungeKutta and Multistep Time Discretizations, World Scientific Press, 2011.

[26] J. F. B. M. Kraaijevanger, Contractivity of Runge-Kutta methods, BIT, 31 (1991), pp. 482-528.

[27] E. J. Kubatko, B. A. Yeager, and D. I. Ketcheson, Optimal strong-stabilitypreserving runge-kutta time discretizations for discontinuous galerkin methods, J. Sci. Comput., 60 (2014), pp. 313-344.

[28] F. Kupka, N. Happenhofer, I. Higueras, and O. Koch, Total-variation-diminishing implicit-explicit runge-kutta methods for the simulation of double-diffusive convection in astrophysics, J. Comput. Phys., 231 (2012), pp. 3561-3586.

[29] L. Pareschi and G. Russo, Implicit-explicit Runge-Kutta schemes and applications to hyperbolic systems with relaxation, Journal of Scientific Computing, 25 (2005), p. 129Ð155. [OpenAIRE]

[30] S. J. Ruuth and R. J. Spiteri, Two barriers on strong-stability-preserving time discretization methods, Journal of Scientific Computation, 17 (2002), pp. 211-220. [OpenAIRE]

[31] C.-W. Shu, Total-variation diminishing time discretizations, SIAM J. Sci. Stat. Comp., 9 (1988), pp. 1073-1084.

[32] C.-W. Shu and S. Osher, Efficient implementation of essentially non-oscillatory shockcapturing schemes, Journal of Computational Physics, 77 (1988), pp. 439-471. [OpenAIRE]