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Open image in new window Fig. 2 Absolute errors of Example 3 for (S=48).
A comparison between the absolute errors of Example 3 for different values of α, β is explained at x = 1 in Table 3.
In Table 1 we list the maximum pointwise error of Example 1, while in Table 2, we compare the best errors of Example 1.
end{aligned}Using the hybrid method with (Q=5, P=5,10,20) for (sin (0,1)), the maximum absolute errors of Example 6 are reported in Table 5.
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Figure 2 The relative error of Example 4.2 ( n = 21, N = 5).
Figure 3 The absolute error of Example 4.2 ( n = 51, N = 5).
Open image in new window Fig. 1 The absolute error of Example 2 for (sigma =frac{1}{4}).
We find that the method (3.7) is more accurate than the Runge-Kutta methods for large N. Figure 2 The absolute error of Example ( 4.1 ).
We find again that the method (3.7) is more accurate than the corresponding Runge-Kutta methods for large N. Figure 4 The absolute error of Example ( 4.2 ).
The numerical results are given in Figures 1, 2, 3, and 4. Figure 1 The absolute error of Example 4.2 ( n = 21, N = 5).
Now we may give Table 5 which is expressed that absolute error of Example 2.1 for different values of λ and γ with x = 0.2, x = 0.4 and x = 0.6 respectively.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com