I have been interested in the derivation of new and better Runge-Kutta algorithms for some time. In particular, I showed that the design of Runge-Kutta pairs by E. Fehlberg could be improved to ...

SIAM Journal on Numerical Analysis, Vol. 34, No. 1 (Feb., 1997), pp. 22-47 (26 pages) We suggest a general method for the construction of highly continuous interpolants for one-step methods applied to ...

Semi-explicit Runge-Kutta methods of order 3 with four stages and order 4 with five stages are discussed, from stability point of view. Some A-stable and L-stable subclasses of such methods are ...