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. 31, No. 3 (Jun., 1994), pp. 876-891 (16 pages) The mono-implicit Runge-Kutta methods are a subclass of the well-known implicit Runge-Kutta methods and have ...