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Bibliography

Books

[butcher2003]J.C. Butcher, Numerical Methods for Ordinary Differential Equations
[hairer1993]Hairer & Wanner, Solving Ordinary Differential Equations I: Nonstiff Problems
[hairer1993b]Hairer & Wanner, Solving Ordinary Differential Equations II: Stiff Problems
[leveque2007]R.J. LeVeque, Finite Difference Methods for Ordinary and Partial Differential Equations

Journal Articles

[albrecht1996]Albrecht, The Runge-Kutta Theory in a Nutshell, (1996) p. 1727
[butcher1997]J.C. Butcher & S. Tracogna, “Order Conditions for Two-Step Runge-Kutta methods”, APNUM 24 pp. 351-364 (1997)
[dutt2000]
  1. Dutt & L. Greengard & V. Rokhlin, Spectral deferred correction methods for ordinary differential equations, BIT 40:241-266 (2000)
[enright1987]W.H. Enright & J.D. Pryce, Two FORTRAN Packages for Assessing Initial Value Methods, ACM Trans. on Mathematical Software 13(1):1-27 (1987)
[gottlieb2009]Gottlieb, Ketcheson, & Shu, High Order Strong Stability Preserving Time Discretizations, J. Sci. Comput. 38(3):251 (2009)
[higueras2005]
  1. Higueras, Representations of Runge-Kutta methods and strong stability preserving methods, SINUM 43 pp. 924-948 (2005)
[kennedy2000]C.A. Kennedy & M.H. Carpenter & R.M. Lewis, Low-storage, explicit Runge-Kutta schemes for the compressible Navier-Stokes equations, APNUM 35:177-219 (2000)
[ketcheson2010]D.I. Ketcheson Runge–Kutta Methods with Minimum Storage Implementations, J. Comput. Phys. 229:1763-1773 (2010)
[ketcheson2009c]D.I. Ketcheson & Sigal Gottlieb & Colin B. Macdonald Strong Stability Preserving Two-step Runge–Kutta Methods
[kraaijevanger1991]JFBM Kraaijevanger, Contractivity of Runge-Kutta Methods, BIT 1991
[ketcheson2008]D.I. Ketcheson, Highly efficient strong stability preserving Runge-Kutta methods with low-storage implementations, SISC 30(4):2113 (2008)
[ketcheson2009]D.I. Ketcheson, C.B. Macdonald, and S. Gottlieb, Optimal implicit strong stability preserving Runge-Kutta methods, APNUM 59(2):373 (2009)

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