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The quality of the approximation for the second moment (variance) is comparable to Roberts' approximation for the individual blocking probabilities.
Recipe 1 is to use the finite difference approximation for the second order derivatives at a nearby interior grid point, whenever this is possible.
It is now necessary to define an approximation for the second boundary condition of (1.2).
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After a transformation of the original problem, the L1 discretization is applied for the time-fractional part and fourth-order accuracy compact approximation for the second-order space derivative.
Firstly, we discuss the semi-discrete mixed finite element approximation for the fourth order parabolic optimal control problem in Section 2.
Numerical solutions have been presented in Table 3. Numerical results at (t=2) and (t=4) show that our results are better than the results obtained using second-order approximations for the second derivative.
Using these equations, we achieved a good approximation for extending the first and second free energies of electron transfer (ΔGet(n); n = 1,2 in kcal mol-1) for the other [SWCNT 5,5 -armchair-C n H20][SWCNT 5,5 -armchair-C200 to 300) 131 to 141.
In this paper, we propose finite difference approximations for the fourth-order time-dependent parabolic PDEs (1) and (6).
Using the approximations for the first two moments of X2 or X 2 ∗ found previously, the minimum waiting time of LP packets can be found using the Pollaczek Khinchine relation[26].
This is a consequence of the connection between the bounds, the Liouville-Green approximation for the associated second order ODE and the asymptotic behavior of the associated three-term recurrence relation.
The bounds are related to the Liouville-Green approximation for the associated second order ODEs as well as to the asymptotic behavior of the associated three-term recurrence relation as n → +∞; the bounds are sharp both as a function of n and x.
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