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Exact(17)
Let us denote the probability of having made an error at time by.
We can then estimate the probability of having an error at time as follows: (17).
Letting represent the mean value of, the RMS of the total error at time is given by.
Letting represent the mean value of ϕ i, the RMS of the position error at time is given by.
By contrast, a value of (hat {E}_{k}) close to 1 corresponds to the maximum possible estimation error at time step k.
An inspection of (16) will immediately show that if the convergence does occur, the root mean-squared estimation error at time is such that (18).
Similar(41)
The exact solutions together with its approximate solutions and corresponding errors at time (T=1) with (alpha=0.99, Delta x= Delta y =0.1,Delta t=0.1) are represented graphically in Figure 2.
Figure 5 shows the graphs of resulting absolute errors at time (t=1) with (alpha=0.99, N=121,Delta t=0.1,{Re}=10) for both regular and irregular distributions.
The distributions of the errors at time t = 10 and t = 20 are shown graphically for solitary wave amplitudes 1 and 0.3 in Figure 3.
In this example, we choose uniform mesh to compute the maximum absolute errors at time (t = 1) for a fixed (k = 0.01), (p = 1) and 2 and for various values of (R_{e} = varepsilon^{ - 1}).
where f m (n) and b m (n) denote the M th stage forward and backward prediction errors at time n, respectively, and κ m (n) is the reflection coefficient.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com