A curiosity of low-order explicit Runge-Kutta methods

Oliver, J.

doi:10.1090/S0025-5718-1975-0391514-5

Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

A curiosity of low-order explicit Runge-Kutta methods
HTML articles powered by AMS MathViewer

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