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Fig. 10 Relation between the absolute error and NN distance from the training samples for each test sample.

Tables 1 and 2 show the comparison between the absolute error of exact and approximate solutions for various values of M with (k=2, 3).

Table 1 shows the comparison between the absolute error of exact and approximate solutions for various values of M (with k = 2 ).

Table 9 shows the comparison between the absolute error of exact and approximate solutions for various values of M with (k=2, 3).

Because SVR is a type of example-based regression approach, we first present Fig. 10 to investigate the relation between the absolute error and the NN distance from the training samples for each test sample, that is, we want to determine whether a rare test sample that is far from any training samples suffers from large errors.

The comparison between the absolute errors of the proposed method and that developed by Viswanadham and Ballem [22] is shown in Table 1 and Fig. 1, respectively.

The comparison between the absolute errors of the proposed method and that developed by Ballem and Viswanadham [26] is shown in Table 2 and Fig. 2, respectively.

A comparison between the absolute errors of Example 3 for different values of α, β is explained at x = 1 in Table 3.

For several points, a comparison between the absolute errors of problem (61) which were obtained using the linearized compact difference method (LCDM [39]) and the results obtained by our method is presented in Table 1 at (N=10).

The paired Wilcoxon test was used to test for differences between the absolute errors of the three estimates.

Then, for each small data set and for each pair of methods, we calculated the difference between the absolute errors.