References
- Ceschino , F. and Kuntzmann , J. 1966 . Numerical Solution of Initial Value Problem , Prentice-Hall .
- England , R. 1969 . Error estimates for Runge-Kutta type solutions to systems of ordinary differential equations . Comp. Journal , 12 : 166 – 170 .
- Enright , W. H. , Hull , T. E. and Lindberg , B. 1975 . Comparing numerical methods for stiff systems of ordinary differential equations . BIT , 15 : 10 – 48 .
- Fehlberg , E. 1970 . Klassische Runge-Kutta-Formeln vierter und niedrigere Ordnung mit Schrittweiten-Kontrolle und ihre Answendung auf Wärmeleitungs probleme . Computing , 6 : 61 – 71 .
- Felberg E. Classical fifth, sixth, seventh, and eight order Runge-Kutta formulas with stepsize control NASA Technical Report No. 287 1968
- Fehlberg , E. 1969a . Klassische Runge-Kutta Formeln fünfter und siebenter Ordnung mit Schrittweiten-Kontrolle . Computing , 4 : 93 – 106 .
- Gear , C. W. 1969 . The automatic integration of stiff ordinary differential equations . Information Processing , 68 : 187 – 193 .
- Hull , T. E. , Enright , W. H. , Fellen , B. M. and Sedgwick , A. E. 1972 . Comparing numerical methods for ordinary differential equations . SIAM J. Numer. Anal. , 9 : 603 – 637 .
- Jackson , K. R. , Enright , W. H. and Hull , T. E. 1978 . A theoretical criterion comparing Runge-Kutta formulas . SIAM J. Numer. Anal. , 15 : 618 – 641 .
- Kuntzmann , J. 1957 . Evaluation de l’erreur sur un pas dans les méthodes a pas séparés . Chiffres , 2 : 97 – 102 .
- Kutta , W. 1901 . Beitrag zur näherungsweisen integrations totaler differential gleichungen . Z. Math. Phys. , 46 : 435 – 453 .
- Lambert , J. D. 1973 . Computational methods in ordinary differential equations , John Wiley and Sons .
- Merson , R. H. 1957 . Proc. Symp. on Data Processing, Weapons Research Establishment . An operational method for the study of integration processes . 1957 , Salisbury, South Australia.
- Prothero , A. 1969 . “ Local error estimates for variable step Runge-Kutta methods ” . In Conference on the Numerical Solution of Differential Equations , Springer-Verlag .
- Richardson , L. F. 1927 . The deferred approach to the limit, I-single lattice . Trans. Roy. Soc. London , 226 : 299 – 349 .
- Scraton , R. E. 1964 . Estimation of the truncation error in Runge-Kutta and allied processes . Comp. Journal , 7 : 246 – 248 .
- Shampine , L. E. and Watts , H. A. 1971 . Comparing error estimators for Runge-Kutta methods . Math. Comp. , 25 : 445 – 455 .
- Shintani , H. 1966 . Two-step processes by one-step methods of order 3 and 4 . J. Sci. Hiroshima Univ. Ser. A-1 Math. , 30 : 183 – 195 .
- Shintani , H. 1966 . On a one-step method of order 4 . J. Sci, Hiroshima Univ. Ser. A-1 Math. , 30 : 91 – 107 .
- Zonneveld J. A. Automatic numerical integration Math. Centre Tracts, No. 8, Mathematische Centrum, Amsterdam MR 30, No. 1612 1964