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Furthermore, we apply adaptive time-step controllers based on the embedded temporal error predictors.
However, the temporal error is dominated by the operator splitting error, which is second order for Strang splitting.
Moreover, the spatial and temporal error components can be balanced by time step and space mesh adaptation.
At temporal error tolerances consistent with engineering simulation, ϵ≈10−1 10−2, first-order implicit Euler (BDF1) is uncompetitive.
The temporal error estimators are applied within one time step and the spatial error estimators at a time point.
For unsteady flows, the PCEXP scheme generates a temporal error much smaller than the BDF2 scheme does, while maintaining the expected acceleration at the same time.
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It reduces temporal errors and generates accurate numerical solutions even if large time and coarse spatial step sizes are used in computation.
The spatial and temporal errors are examined and it is shown that the method is globally second order accurate both in time and space.
This could be due to the fact that the forecast accuracy measured in terms of both the amplitude and phase or temporal errors and the forecast precision/reliability quantified in terms of the uncertainty significantly deteriorate with the increase of the lead-time.
The results for the healthy subjects of this pilot study demonstrated that the proposed VRA was efficacious in facilitating the acquisition of task-related motor skills (with almost half trials) and in reducing temporal errors of the desired velocity (by approximately 40%).
We further test the temporal errors and convergence orders.
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