Theory and Modern Applications
Table 4 Comparison of \(L_{\infty } \) errors of Example 1, for various values of x
|  | Legendre wavelet method in [11] (α = 0.75) | Gegenbauer wavelet Galerkin method (β = 1/2,α = 0.75) | Gegenbauer wavelet Galerkin method (β = 1/2,α = 0.90) |
|---|---|---|---|
x | \(L_{\infty } \) | \(L_{\infty } \) | \(L_{\infty } \) |
0.1 | 9.57606e -2 | 8.55547702219717e–3 | 4.51445591132160e–3 |
0.2 | 5.85324e -2 | 6.79113832036982e–3 | 3.11622146809487e–3 |
0.3 | 3.19023e -2 | 6.02803684752118e–3 | 2.54162812421266e–3 |
0.4 | 4.06402e -2 | 6.08029490365147e–3 | 2.64328797967528e–3 |
0.5 | 3.80953e -2 | 6.69028888876044e–3 | 3.21692323448264e–3 |
0.6 | 6.76929e -2 | 7.53122370284809e–3 | 4.00340828863466e–3 |
0.7 | 1.00724e -1 | 8.21039734591478e–3 | 4.69135794213144e–3 |
0.8 | 1.36832e -1 | 8.27312581796025e–3 | 4.92023909497280e–3 |
0.9 | 1.75597e -1 | 7.20728461898440e–3 | 4.28397314715895e–3 |
1.0 | 2.16518e -1 | 4.44842734898737e–3 | 2.33499309868973e–3 |