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On Runge-Kutta processes of high order

Published online by Cambridge University Press:  09 April 2009

J. C. Butcher
Affiliation:
University of Canterbury, New Zealand.
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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.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1964

References

[1]Butcher, J. C., Coefficients for the study of Runge-Kutta integration processes, This Journal 3 (1963), 185201.Google Scholar
[2]Kutta, W., Beitrag zur näherungsweisen Integration totaler Differentialgleichungen, Zeit. Math. Physik 46 (1901), 435452Google Scholar
[3]Nyström, E. J., Über die numerische Integration von Differentialgleichungen, Acta Soc. Sci. Fennicae 50, No. 13 (1925).Google Scholar
[4]Huta, A., Une amélioration de la méthode de Runge-Kutta-Nyström pour la résolution numérique des équations différentielles du premier ordre, Acta Fac. Nat. Univ. Commenian. Math. 1 (1956) 201224.Google Scholar
[5]Huta, A., Contribution à la formule de sixième ordre dans la méthode de Runge-Kutta-Nyström, Acta Fac. Nat. Univ. Comenian. Math. 2 (1957), 2124.Google Scholar
[6]Butcher, J. C., On the integration processes of A. Huta, This Journal 3 (1963), 202206.Google Scholar
[7]Butcher, J. C., Integration processes based on Radau quadrature formulas, Math. Comp., 18 (04, 1964).Google Scholar
[8]Butcher, J. C., Implicit Runge-Kutta processes, Math. Comp., 18 (1964), 5064.Google Scholar