Runge-Kutta methods with constrained minimum error bounds
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- by Richard King PDF
- Math. Comp. 20 (1966), 386-391 Request permission
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
- T. E. Hull and R. L. Johnston, Optimum Runge-Kutta methods, Math. Comp. 18 (1964), 306–310. MR 165700, DOI 10.1090/S0025-5718-1964-0165700-6
- Max Lotkin, On the accuracy of Runge-Kutta’s method, Math. Tables Aids Comput. 5 (1951), 128–133. MR 43566, DOI 10.1090/S0025-5718-1951-0043566-3
- Anthony Ralston, Runge-Kutta methods with minimum error bounds, Math. Comp. 16 (1962), 431–437. MR 150954, DOI 10.1090/S0025-5718-1962-0150954-0
Additional Information
- © Copyright 1966 American Mathematical Society
- 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