A Class of Implicit Runge-Kutta Methods for the Numerical Integration of Stiff Ordinary Differential Equations

One-step methods similar in design to the well-known class of Runge-Kutta methods are developed for the efficient numerical integration of both stiff and nonstiff systems of first-order ordinary differential equations The algomthms developed combine accuracy in the hrait h --~ 0 with a large regmn of absolute stabdity and are demonstrated by direct apphcation to certain particular examples.