Theory and Modern Applications
Table 3 Comparison of \(L_{\infty } \) errors of Example 1, for \(\alpha = 1\) and various values of x
|  | Legendre Wavelet Method in [11] | Gegenbauer wavelet Galerkin Method (β = 1/2) | Gegenbauer wavelet Galerkin Method (β = 3/2) |
|---|---|---|---|
x | \(L_{\infty } \) | \(L_{\infty } \) | \(L_{\infty } \) |
0.1 | 2.50855e-3 | 5.89485917379340e–4 | 7.27313861244472e–4 |
0.2 | 2.64995e-3 | 1.89108963468243e–4 | 1.87503238244180e–4 |
0.3 | 2.83828e-3 | 3.46946817421312e–4 | 4.43686707221280e–4 |
0.4 | 3.09695e-3 | 1.02188765043587e–4 | 1.64783845686911e–4 |
0.5 | 3.44474e-3 | 6.57771755357084e–4 | 4.77970446358944e–4 |
0.6 | 3.89591e-3 | 1.43188248208831e–3 | 1.26736536891631e–3 |
0.7 | 4.46022e-3 | 2.05373983571433e–3 | 1.94238352198511e–3 |
0.8 | 5.14289e-3 | 2.22112881623499e–3 | 2.20080990556537e–3 |
0.9 | 5.94439e-3 | 1.59365562365044e–3 | 1.70225071965713e–3 |
1.0 | 6.86019e-3 | 2.03850342039347e–4 | 7.15353642604666e–5 |