On the attainable order of Runge-Kutta methods

Butcher, J. C.

doi:10.1090/S0025-5718-1965-0179943-X

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.

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On the attainable order of Runge-Kutta methods
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Math. Comp. 19 (1965), 408-417 Request permission

References

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, On Runge-Kutta processes of high order, J. Austral. Math. Soc. 4 (1964), 179–194. MR 0165692
Henry A. Antosiewicz and Walter Gautschi, Numerical methods in ordinary differential equations, Survey of numerical analysis, McGraw-Hill, New York, 1962, pp. 314–346. MR 0136075