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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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Linearly-implicit Runge-Kutta methods based on implicit Runge-Kutta methods
Applied Numerical Mathematics, 1993Linearly-implicit Runge-Kutta methods (LIRKM), based on explicit Runge- Kutta schemes, are compared with implicit Runge-Kutta methods (IRKM) which require the solution of nonlinear equations by Newton-like methods. In particular, the consistency of LIRKM is investigated and the numerical expense of IRKM and LIRKM is considered.
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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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Interpolants for Runge-Kutta-Nyström methods
Computing, 1987Hermite interpolation polynomials are developed for use with low order Runge-Kutta-Nyström methods in producing continuous approximate solutions to second order initial value problems. Polynomials of degrees five and four, which interpolate the solution and derivative components, respectively, are easily computable and require no extra stages ...
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Embedded Pseudo-Runge–Kutta Methods
SIAM Journal on Numerical Analysis, 1991This paper deals with embedded pseudo-Runge-Kutta methods and their use in step size control without additional function evaluations. There is a report on results of a number of numerical experiments.
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Runge-Kutta(-Nyström) methods for ODEs with periodic solutions based on trigonometric polynomials
Applied Numerical Mathematics, 1998Beatrice Paternoster
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New modified Runge–Kutta–Nyström methods for the numerical integration of the Schrödinger equation
Computers and Mathematics With Applications, 2010Theodore E Simos
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