GLOBAL ERROR ESTIMATION WITH RUNGE-KUTTA METHODS

An analysis of global error estimation for Runge - Kutta solutions of ordinary differential equations is presented. The basic technique is that of Zadunaisky in which the global error is computed from a numerical solution of a neighbouring problem related to the main problem by some method of interpolation. It is shown that Runge - Kutta formulae which permit valid global error estimation using low-degree interpolation can be developed, thus leading to more accurate and computationally convenient algorithms than was hitherto expected. Some special Runge - Kutta processes up to order 4 are presented together with numerical results. © 1984, by Academic Press Inc. (London) Limited.