A curiosity of low-order explicit Runge-Kutta methods
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- by J. Oliver PDF
- Math. Comp. 29 (1975), 1032-1036 Request permission
Abstract:
By introducing an additional parameter into the first stage of the explicit Runge-Kutta process, new formulae of second and third order are derived, offering improved error bounds in the second-order case.References
- 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
- Anthony Ralston, A first course in numerical analysis, McGraw-Hill Book Co., New York-Toronto-London, 1965. MR 0191070
- J. C. Butcher, Coefficients for the study of Runge-Kutta integration processes, J. Austral. Math. Soc. 3 (1963), 185–201. MR 0152129
- J. C. Butcher, Implicit Runge-Kutta processes, Math. Comp. 18 (1964), 50–64. MR 159424, DOI 10.1090/S0025-5718-1964-0159424-9
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Math. Comp. 29 (1975), 1032-1036
- MSC: Primary 65L05
- DOI: https://doi.org/10.1090/S0025-5718-1975-0391514-5
- MathSciNet review: 0391514