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Exact(9)
Through our new idea of recurrent functions, we develop new sufficient convergence conditions and tighter error bounds.
Second, it allows for tighter error limitation, which is shown to be necessary to avoid rapid error accumulations for simulations on large-scale models with long travel times.
This would place the estimations of 15% change in resistivity as conservative and shows the importance of obtaining high-quality data, as tighter error bars would lead to stronger changes in resistivity.
Moreover, if K 0 is sufficiently smaller than K, which can happen since K K 0 can be arbitrarily large, then the results obtained in this study provide a tighter error analysis than the one in [10].
However, the fourth-order accurate implicit Runge Kutta scheme is found to be the most efficient in terms of computational cost for a given accuracy level as compared to the lower-order schemes, in spite of the added cost per time step, and the benefits of this scheme increase for tighter error tolerances.
In [11], we presented a finer convergence analysis in the setting of Banach spaces than in [12 16] for the method (GNM) with the advantages ((mathcal{A})): tighter error estimates on the distances involved and the information on the location of the solution is at least as precise.
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Matlab's ode15s solver is used with tight error tolerances ((mathrm{RelTol}=mathrm{AbsTol}=10^{-13})).
This distribution shows how this work is the best representative of the studied data with the tightest error distribution.
In addition, tight error limits were needed for close prediction of ignition delay when varying the mixture composition away from that used for the reduction.
When validated using phenomena other than autoignition, such as perfectly stirred reactor and laminar flame propagation, tight error control or more restrictions on the reduction during the sensitivity analysis stage were needed to ensure good agreement.
Assuming the starting point of the second stage to be a deterministic point beyond the atmosphere, the scheme guides the vehicle properly so that it completes the mission within a tight error bound.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com