A NEW TECHNIQUE FOR THE EARLY DETECTION OF STIFFNESS IN COUPLED DIFFERENTIAL-EQUATIONS AND APPLICATION TO STANDARD RUNGE-KUTTA ALGORITHMS

Higher-order Runge-Kutta (RK) algorithms employing local truncation er ror (LTE) estimates have had very limited success in solving stiff dif ferential equations. These LTEs do not recognize stiffness until the r egion of instability has been crossed after which no correction is pos sible. A new technique has been designed, using the local stiffness fu nction (LSF), which can detect stiffness very early before instability occurs. The LSF is a normalized dimensionless ratio which is essentia lly based on the product of the step size and the geometric mean of al l the slopes. It is exceedingly sensitive to the onset of stiffness. T ogether, the LSF and the LTE form a complementary pair which can coope rate to help solve some mildly stiff equations which were previously i ntractable to RK algorithms alone. Examples are given of implementatio n and LSF performance.