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I have a question on the same topic in math.stackexchange.com: https://math.stackexchange.com/questions/664422/how-does-matlab-simulink-get-such-accurate-ode-solution-results, and it remains open.

I am looking to understand how Simulink's accuracy of solving ODEs with purportedly the fourth order Runge-Kutta solver (ODE4) far exceeds any implementation I have developed so far. Either I have incorrectly implemented the algorithm or Simulink is doing extra work behind-the-scenes to increase accuracy. I have asked on the math stack exchange site about potential mathematical methods, I ask here about computer science methods of achieving increased accuracy.

My interest comes from a need to understand model stability using different solution methods, and not knowing what Simulink is doing to get accuracy means having less idea of its potential stability in certain situations.

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J Collins
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    The difference was caused by an implementation error as explained in the duplicate question: http://math.stackexchange.com/a/664511/104019 – Daniel Feb 05 '14 at 12:24

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I think that this has some connection with energy conservation of integration method.

They are probably using modified RK method without such energy drift.

http://en.wikipedia.org/wiki/Symplectic_integrator

Luka Rahne
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The simple Runge-Kutta method as it turns out is as accurate as the Simulink definition when implemented correctly. Several implementation errors contributed to a relatively small but definite error from the correctly implemented solution.

The answer to this question is that Simulink implements the RK solver as agreed in literature with no proprietary improvement.

J Collins
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