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The results in this table show that with few numbers of retained modes we obtained a maximum pointwise error of order 10−8.
Table 4 lists the maximum pointwise error and maximum absolute relative error of using BGM and BPG with various choices of.
Table 1 lists the maximum pointwise error and maximum absolute relative error of using the BGM and BPGM with various choices of.
In Table 1 we list the maximum pointwise error of Example 1, while in Table 2, we compare the best errors of Example 1.
In Table 2, we list the maximum pointwise error E and the time elapsed τ for different values of M. The results in this table show that with few numbers of retained modes we obtained a reasonable accuracy 10−13.
The error estimation is given to show the accuracy of approximation, and the following maximum pointwise error between the exact and approximate solution is given: Vert cdot Vert _{infty}=mathop{mathrm{Max}}_{i,n} biglvert u_{mathrm{app}}(x_{i},t_{n} -u_{mathrm{ex}}(x_{i},t_{n} -u_{mathrm{ex}d i=-N,ldots,N, n=0,1,ldots,M.
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For any values of and, the maximum pointwise errors and the -uniform are calculated using (5.10).
Figure 3 The global maximum pointwise errors at (pmb{N=4}) and (pmb{Delta t=10^{-3}}) (a) by using the Linsolve package, (b) by using of Tikhonov regularization.
In addition, the maximum pointwise errors in the solution by SMLP and SMTR in Table 4 are plotted in Figure 9 and Figure 10.
Figure 6 The global maximum pointwise errors at (pmb{N=32}) and (pmb{Delta t=10^{-6}}) (a) by using the Linsolve package, (b) by using Tikhonov regularization.
In Table 5, we list the maximum absolute errors using GJCOMM for various values of N. Let E denote the maximum pointwise errors if the selected collocation points are the zeros of the polynomial (tilde{R}^{(2,2)}_{N+1}(x)).
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