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.
John Keevil (2019). ODE4 gives more accurate results than ODE45, ODE23, ODE23s (https://www.mathworks.com/matlabcentral/fileexchange/59044-ode4-gives-more-accurate-results-than-ode45-ode23-ode23s), MATLAB Central File Exchange. Retrieved .
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