New Runge-Kutta algorithms are developed which determine the solution of a system of ordinary differential equations at any point within a given integration step, as well as at the end of each step.

SIAM Journal on Numerical Analysis, Vol. 43, No. 3 (2006), pp. 924-948 (25 pages) Over the last few years a great effort has been made to develop monotone high order explicit Runge-Kutta methods by ...