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A parallel Runge-Kutta integration method
Parallel Computing, 1989Abstract In this paper, the development of parallel integration methods of Runge-Kutta form for the step by step solution of ordinary differential equations is presented.
David J. Evans 0001, Bahrom Sanugi
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2019
The class of differential equations for which explicit solutions can be obtained is rather small. In fact, in Chap. 3, we have already remarked that to find an explicit solution of the second-order linear differential equation ( 3.2) there does not exist any method.
Ravi P. Agarwal +2 more
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The class of differential equations for which explicit solutions can be obtained is rather small. In fact, in Chap. 3, we have already remarked that to find an explicit solution of the second-order linear differential equation ( 3.2) there does not exist any method.
Ravi P. Agarwal +2 more
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Runge–Kutta–Chebyshev projection method
Journal of Computational Physics, 2006In this paper a fully explicit, stabilized projection method called the Runge-Kutta-Chebyshev (RKC) projection method is presented for the solution of incompressible Navier-Stokes systems. This method preserves the extended stability property of the RKC method for solving ODEs, and it requires only one projection per step.
Zheming Zheng, Linda R. Petzold
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1973
One-step methods (see Def. 2.1.8) form a particularly simple class of f. s. m. for IVP 1. Among these, a certain class of methods has commonly been associated with the names of C. Runge and W. Kutta and is widely used. These “Runge-Kutta methods” (RK-methods) are 1-step m+1-stage methods in the sense of Def. 2.1.10.
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One-step methods (see Def. 2.1.8) form a particularly simple class of f. s. m. for IVP 1. Among these, a certain class of methods has commonly been associated with the names of C. Runge and W. Kutta and is widely used. These “Runge-Kutta methods” (RK-methods) are 1-step m+1-stage methods in the sense of Def. 2.1.10.
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Families of Imbedded Runge–Kutta Methods
SIAM Journal on Numerical Analysis, 1979Using the s stages of an explicit Runge–Kutta method of order p, approximations of various lower orders may be obtained. A linear system of equations classifies and characterizes parameters of all properly imbedded methods.For all methods with $p = 2,3$, and some with $p = 5$, and s minimal, approximations of all lower orders may be obtained. Otherwise,
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Runge-Kutta(-Nyström) methods for ODEs with periodic solutions based on trigonometric polynomials
Applied Numerical Mathematics, 1998Paternoster B
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Order conditions for Two-Step Runge-Kutta methods
Applied Numerical Mathematics, 1997J C Butcher
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Symplectic conditions for exponential fitting Runge-Kutta-Nyström methods
Mathematical and Computer Modelling, 2005Vigo Aguiar, Angel Tocino
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