Keywords
explicit and implicit methods
interpolation
pseudo-algorithms
parametric schema
Métodos de Runge-Kutta n-dimencionales
explícitos e implícitos
interpolación
cuasi algoritmos
esquema paramétrico
How to Cite
Abstract
We present the Runge-Kutta methods of several one-step levels in Rn , as well as algorithms in pseudo-code for the implicit and explicit methods. We study the problem of error control in Rn and we give numerical examples in tables or parameter schemata.
References
Albrecht, P. (1987) “A new theoretical approach to Runge-Kutta methods”, SIAM Journal Numerical Analysis 24(2).
Arguedas, V.; Mata, R. (1992) “Un teorema sobre el orden de los métodos de Runge-Kutta”, Ciencias Matemáticas, U.C.R.3(1).
Burden, R.; Faires, D. (1985) Análisis Numérico. Editorial Iberoamérica, México.
Collatz, L. (1960) The Numerical Treatment of Differential Equations. Springer-Verlag, Heidelberg.
Fehlberg, E. (1970) “Klassische Runge-Kutta Formeln vierter und niedrigerer Ordnung mit Schrittweiten-Kontrolle und ihre Anwendung auf Wärmeleitungs-probleme”, Computing 6: 61–71.
Hairer, E.; Iserles, A.; Sanz-Serna, J.M. (1990) “Equilibria of Runge-Kutta methods”, Numerische Mathematik 58: 243–254.
Kansy, K. (1973) “Elementare Fehlerdarstellung für Ableitungen bei der Hermite-Interpolation”, Numer. Math.21: 350–354.
Mata, R. (1990) Algunos Aspectos Teóricos de los Métodos Runge-Kutta. Tesis de Licenciatura, Universidad de Costa Rica.
Press, W.; Flannery, B.; Teukolsky, S.; Vetterling, W. (1987) Numerical Recipes, USA.
Press, W.; Flannery, B.; Teukolsky, S.; Vetterling, W. (1987) Numerical Recipes, Example Book (Fortran), USA.
Shampine, L.F.; Gordon, M.K. (1975) Computer Solution of Ordinary Differential Equations: the Initial Value Problem. W. H. Freeman, San Francisco.
Shampine, L.F.; Watts, H.A. (1976) “Practical solution of ordinary differential equations by Runge-Kutta methods”, Rept. SAND 76-0585, Sandía National Laboratories, Albuquerque, N. M.
Shampine, L. F. (1985) “Interpolation for Runge-Kutta methods”, SIAM Journal Numerical Analysis 22(5).
Stoer, J.; Burlisch, R. (1990) Numerische Mathematik 2.Tercera edición, Springer-Verlag, Berlin.
Werner, H.; Schabach, R. (1972) Praktische Mathematik II. Springer-Verlag, Berlin.