New Runge-Kutta methods for initial value problems

Abstract

Runge-Kutta methods for solving initial value problems of the form y′ = f(x,y) can be reassessed by geometric mean (rather than arithmetic mean) averaging of the functional values in the integrational interval. Initially a low order accuracy formula is obtained but by recomparing the Taylor series expansions in terms of the functional derivatives, new weighting parameters can be obtained to yield new Runge-Kutta formulae of 3rd and 4th order. © 1989.