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For periodic simulation, please use "conserve energy". This is because, any minor change in S can result in huge difference when many periods are used. as you can see, (S+ds)^N so when N is large the error will be amplified significantly.
On the other hand, the convergence testing can be challenge:
Understanding EME error diagnostics
Convergence Testing - Error Diagnostics - Method for Using Diagnostics
EME Convergence Testing - An Intuitive Approach
Convergence testing process for EME simulations
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