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Runge-Kutta methods with constrained minimum error bounds


Author: Richard King
Journal: Math. Comp. 20 (1966), 386-391
MSC: Primary 65.60
DOI: https://doi.org/10.1090/S0025-5718-1966-0203947-2
MathSciNet review: 0203947
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Abstract: Optimum Runge-Kutta methods of orders $ m = 2,3$, and $ 4$ are developed for the differential equation $ y' = f(x,y)$ under Lotkin's conditions on the bounds for $ f$ and its partial derivatives, and with the constraint that the coefficient of $ {\partial ^m}f/\partial {x^m}$ in the leading error term be zero. The methods then attain higher order when it happens that $ f$ is independent of $ y$.


References [Enhancements On Off] (What's this?)

  • [1] T. E. Hull & R. L. Johnston, "Optimum Runge-Kutta methods," Math. Comp., v. 18, 1964, pp. 306-310. MR 29 #2980. MR 0165700 (29:2980)
  • [2] M. Lotkin, "On the accuracy of Runge-Kutta's method," MTAC, v. 5, 1951, pp. 128- 133. MR 13, 286. MR 0043566 (13:286c)
  • [3] A. Ralston, "Runge-Kutta methods with minimum error bounds," Math. Comp., v. 16, 1962, pp. 431-437; Corrigendum, v. 17, 1963, p. 488. MR 27 #940. MR 0150954 (27:940)

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DOI: https://doi.org/10.1090/S0025-5718-1966-0203947-2
Article copyright: © Copyright 1966 American Mathematical Society

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