Solution of structured non-stiff ODEs

摘要

The solution of the initial value problem for a system of ordinary differential equations (ODEs), y′ = f(x, y), by Runge-Kutta methods is considered. The structure to be exploited is that a large portion of the cost of evaluating f(x, y) arises in the evaluation of functions of the independent variable x only. It is shown that when the structure is favorable, there are methods which are considerably more efficient than those currently used in general purpose codes.