An implicit one-step method of high-order accuracy for the numerical integration of ordinary differential equations

Abstract

For a differential equationdx/dt=f(t, x) withf t (t, x),f x (t, x) computable, the author presents a new one-step method of high-order accuracy. A rule of controlling the mesh size is given and the method is compared with the Runge-Kutta method in two numerical examples.