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Coefficients for the study of Runge-Kutta integration processes

  • J. C. Butcher (a1)
Abstract

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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References
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[1]Runge C., Über die numerische Auflösung von Differentialgleichungen. Math. Ann. 46 (1895), 167178.
[2]Kutta W., Beitrag zur näherungsweisen Integration totaler Differentialgleichungen. Zeit. Math. Physik, 46 (1901), 435452.
[3]Nyström E. J., Über die numerische Integration von Differentialgleichungen. Acta Soc. Sci. Fennicae 50, No. 13 (1925).
[4]Gill S., A process for the step-by-step Integration of Differential Equations in an Automatic Digital Computing Machine. Proc. Camb. Phil. Soc. 47 (1951), 96108.
[5]Merson R. H., An operational method for the study of integration processes. Proceedings of conference on data processing and Automatic Computing Machines at Weapons Research Establishment, Salisbury, South Australia (1957).
[6]Polya G. and Szegö G., Aufgaben und Lehrsätze aus der Analysis I, p. 301. Grind. Math. Wiss. 19 (Springer, 1925).
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Journal of the Australian Mathematical Society
  • ISSN: 1446-7887
  • EISSN: 1446-8107
  • URL: /core/journals/journal-of-the-australian-mathematical-society
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