Coefficients for the study of Runge-Kutta integration processes

@article{Butcher1963CoefficientsFT,
  title={Coefficients for the study of Runge-Kutta integration processes},
  author={John C. Butcher},
  journal={Journal of the Australian Mathematical Society},
  year={1963},
  volume={3},
  pages={185 - 201}
}
  • J. Butcher
  • Published 1 May 1963
  • Mathematics
  • Journal of the Australian Mathematical Society
We consider a set of η first order simultaneous differential equations in the dependent variables y1, y2, …, yn and the independent variable x ⋮ No loss of gernerality results from taking the functions f1, f2, …, fn to be independent of x, for if this were not so an additional dependent variable yn+1, anc be introduced which always equals x and thus satisfies the differential equation 
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386 Citations
Highly Influential Citations
33
Background Citations
67
Methods Citations
107
Results Citations
1

386 Citations

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On Runge-Kutta processes of high order

  • J. Butcher
  • Mathematics
    Journal of the Australian Mathematical Society
  • 1964
An (explicit) Runge-Kutta process is a means of numerically solving the differential equation , at the point x = x0+h, where y, f may be vectors.

B-Series Analysis of Stochastic Runge-Kutta Methods That Use an Iterative Scheme to Compute Their Internal Stage Values

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A unifying approach is employed for the construction of stochastic B-series which is valid both for It o- and Stratonovich-stochastic differential equations (SDEs) and applicable both for weak and strong convergence to analyze the order of the iterated Runge-Kutta method.

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Runge–Kutta (RK)-methods are treated here as linear multistage methods within the author’s concept of A-methods, and it is shown how the order of a RK-method depends on the error constants of its stages.
...

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