Computer derivation of algebraic equations associated with runge-kutta formulas
- 24 Downloads
The derivation of algebraic non-linear equations associated with Runge-Kutta formulas increases in complexity as the order of these formulas increases. To overcome this difficulty various operational methods have been devised. But these methods are quite involved and there also exists the possibility of human errors which may be difficult to detect. The aim of this paper is the derivation of these algebraic equations through a digital computer, the IBM 7094, using Fortran IV. The technique employed is based upon a mathematical method established by the first author. With the advent of the space age there arose a continuous need for Runge-Kutta formulas of higher and higher orders. It seems that the computer offers the best, if not the only, hope in keeping up with these needs.
Key wordsAlgebraic equations Runge-Kutta computer derivation
Unable to display preview. Download preview PDF.
- 1.Butcher, J. C.,Coefficients for the Study of Runge-Kutta Processes, J. Australian Math. Soc. Vol. 3, 1963, pp. 185–201.Google Scholar
- 2.Collatz, L.,The Numerical Treatment of Differential Equations, Third Edition, Springer-Verlag, Berlin, 1960, pp. 17–18 and p. 66.Google Scholar
- 3.Huta, A., Acta Facultatis Rerum Naturalium Universitatis Comenianae, 1965, Tom. 1, Fasc. IV–VI, pp. 201–224.Google Scholar
- 4.Milne, W. E.,Numerical Solution of Differential Equations, John Wiley and Sons, New York, London, 4th Printing, 1962, p. 74.Google Scholar
- 5.Sarafyan, D.,Improvements in the Derivation of Runge-Kutta Formulas and Computer Implementations, Louisiana State University in New Orleans Technical Report No. 4, December 1965.Google Scholar