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. 53, No. 1 (2015), pp. 17-42 (26 pages) This work considers a general structure of the additively partitioned Runge–Kutta methods by allowing for different ...

The study of the sensitivity of the solution of a system of differential equations with respect to changes in the initial conditions leads to the introduction of an adjoint system, whose ...