Computation of optimal monotonicity preserving general linear methods

Mathematics of Computation

Volumn 78, Issue 267, 2009, Pages 1497-1513

  Ketcheson, David I ^a  

^a UNIVERSITY OF WASHINGTON   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 67749146997     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-09-02209-1     Document Type: Article

References (26)

1. J.C. Butcher. Numerical Methods for Ordinary Differential Equations. Wiley, 2003. MR1993957 (2004e:65069)
2. M.-H. Chen, B. Cockburn, and F. Reitich. High-order RKDG methods for computational electromagnetics. Journal of Scientific Computing, 22-23:205-226, 2005. MR2142195 (2005m:65208)
3. Bernardo Cockburn, Jianliang Qian, Fernando Reitich, and Jing Wang. An accurate spectral/discontinuous finite-element formulation of a phase-space-based level set approach to geometrical optics. Journal of Computational Physics, 208:175-195, 2005. MR2144697 (2006a:65124)
4. D. Gottlieb and E. Tadmor. The CFL condition for spectral approximations to hyperbolic initial-boundary value problems. Mathematics of Computation, 56:565-588, 1991. MR1066833 (91k:65137)
5. Sigal Gottlieb. On high order strong stability preserving Runge-Kutta and multi step time discretizations. Journal of Scientific Computing, 25:105-127, 2005. MR2231945 (2007f:65029)
6. Sigal Gottlieb and Lee-Ad J. Gottlieb. Strong stability preserving properties of Runge-Kutta time discretization methods for linear constant coefficient operators. Journal of Scientific Computing, 18:83-109, 2003. MR1958936 (2003m:65161)
7. Sigal Gottlieb, David I. Ketcheson, and Chi-Wang Shu. High order strong stability preserving time discretizations. Journal of Scientific Computing, DOI: 10.1007/s10915-008-9239-z.
8. Sigal Gottlieb and Steven J. Ruuth. Optimal strong-stability-preserving time-stepping schemes with fast downwind spatial discretizations. Journal of Scientific Computing, 27:289-303, 2006. MR2285782 (2008j:65122)
9. Sigal Gottlieb and Chi-Wang Shu. Total variation diminishing Runge-Kutta schemes. Mathematics of Computation, 67:73-85, 1998. MR1443118 (98c:65122)
10. Sigal Gottlieb, Chi-Wang Shu, and Eitan Tadmor. Strong stability preserving high-order time discretization methods. SIAM Review, 43:89-112, 2001. MR1854647 (2002f:65132)
11. E. Hairer, S.P. Norsett, and G. Wanner. Solving ordinary differential equations I: Nonstiff Problems. Springer Series in Computational Mathematics. Springer, Berlin, 1993. MR1227985 (94c:65005)
12. C. Huang. Strong stability preserving hybrid methods. Applied Numerical Mathematics, 2008. doi: 10.1016/j.apnum.2008.03.030.
13. Rolf Jeltsch and Olavi Nevanlinna. Stability of explicit time discretizations for solving initial value problems. Numerische Mathematik, 37:61-91, 1981. MR615892 (82g:65042)
14. David I. Ketcheson. Highly efficient strong stability preserving Runge-Kutta methods with low-storage implementations. SIAM Journal on Scientific Computing, 30(4):2113-2136, 2008. MR2407154
15. David I. Ketcheson. Strong stability preserving two-step Runge-Kutta methods, 2008, in preparation.
16. David I. Ketcheson, Colin B. Macdonald, and Sigal Gottlieb. See the SSP website: http://www.cfm.brown.edu/people/sg/ssp.html.
17. J. F. B. M. Kraaijevanger. Absolute monotonicity of polynomials occurring in the numerical solution of initial value problems. Numerische Mathematik, 48:303-322, 1986. MR826471 (87c:65084)
18. J. F. B. M. Kraaijevanger. Contractivity of Runge-Kutta methods. BIT, 31:482-528, 1991. MR1127488 (92i:65120)
19. H W. J. Lenferink. Contractivity-preserving explicit linear multistep methods. Numerische Mathematik, 55:213-223, 1989. MR987386 (90f:65058)
20. H W. J. Lenferink. Contractivity-preserving implicit linear multistep methods. Math. Comp., 56:177-199, 1991. MR1052098 (91i:65129)
21. Tiao Lu, Wei Cai, and Pingwen Zhang. Discontinuous Galerkin time-domain method for GPR simulation in dispersive media. IEEE Transactions on Geoscience and Remote Sensing, 43(1):72-80, 2005.
22. Steven J. Ruuth and Willem Hundsdorfer. High-order linear multistep methods with general monotonicity and boundedness properties. Journal of Computational Physics, 209:226-248, 2005. MR2145787 (2005m:65143)
23. J. Sand. Circle contractive linear multistep methods. BIT, 26:114-122, 1986. MR833836 (87h:65124)
24. C.-W. Shu and S. Osher. Efficient implementation of essentially non-oscillatory shockcapturing schemes. Journal of Computational Physics, 77:439-471, 1988. MR954915 (89g:65113)
25. M. N. Spijker. Contractivity in the numerical solution of initial value problems. Numerische Mathematik, 42:271-290, 1983. MR723625 (85b:65067)
26. J. A. van de Griend and J. F. B.M. Kraaijevanger. Absolute monotonicity of rational functions occurring in the numerical solution of initial value problems. Numerische Mathematik, 49:413-424, 1986. MR853663 (87m:65102)