Theory and Modern Applications
Table 1 For Example 6.1, a comparison the absolute error results in [15] and [31], in the case \(\alpha =2\), \(\beta =1\), \(T=2\) at \(n=5\), and those in our setting when \(n=3\), \(\phi (h)=0.5 (\exp (2h)-1)\)
From: Vieta–Lucas polynomials for solving a fractional-order mathematical physics model
x | Method in [15] | Method in [31] | Ours |
|---|---|---|---|
0.0 | 2.726 × 10−5 | 2.198 × 10−5 | 2.553 × 10−19 |
0.1 | 3.456 × 10−5 | 2.416 × 10−5 | 3.155 × 10−17 |
0.2 | 3.810 × 10−5 | 2.606 × 10−5 | 5.664 × 10−17 |
0.3 | 3.809 × 10−5 | 2.758 × 10−5 | 7.554 × 10−17 |
0.4 | 3.514 × 10−5 | 2.865 × 10−5 | 8.651 × 10−17 |
0.5 | 3.009 × 10−5 | 2.920 × 10−5 | 9.107 × 10−17 |
0.6 | 2.387 × 10−5 | 2.915 × 10−5 | 8.814 × 10−17 |
0.7 | 1.735 × 10−5 | 2.844 × 10−5 | 7.836 × 10−17 |
0.8 | 1.120 × 10−5 | 2.704 × 10−5 | 5.849 × 10−17 |
0.9 | 5.722 × 10−6 | 2.489 × 10−5 | 3.329 × 10−17 |
1.0 | 7.257 × 10−7 | 2.489 × 10−5 | 2.553 × 10−19 |