Interpolation for Runge–Kutta Methods

Abstract

Runge–Kutta methods provide a popular way to solve the initial value problem for a system of ordinary differential equations. In contrast to the Adams methods, there is no natural way to approximate the solution between mesh points. A way to accomplish this is proposed which is applicable to some important formulas. Its theoretical support is much better than that of interpolation in the popular variable order, variable step Adams codes.