ODE4 gives more accurate results than ODE45, ODE23, ODE23s

Subroutine ode4 is more accurate than ode45, ode23 and ode23s for solving ODE.

The attached scripts solve the Two-Body Orbit Vector Ordinary Differential Equation using a MATLAB supported subroutine ode45, ode23 or ode23s and also using a simple unsupported subroutine ode4 (available in the attachment and elsewhere on File Exchange). All these subroutines use the Runge-Kutta algorithm for solving ODE's. The scripts compare the results with the exact analytic solution which is an appropriate ellipse: we can therefore compare the accuracies of the subroutines. We find that the supported subroutines show errors in the range of 0.1 to 0.5%; whereas ode4 shows a peak error of less than 10^-7% i.e. 10^6 times smaller.These results indicate that ode4 should probably be the first Runge-Kutta subroutine to try for solving ODE's. The attached information contains plots of these results and all the necessary scripts to duplicate the results.