Theory and Modern Applications
Table 1 Numerical results of Example 4.1 using the framelet systems \({{X(\Omega _{1})}}\) and \({{X(\Omega _{2})}}\) for \(m=3\) and \(\lambda =3.25\)
x | Exact | \({{\mathcal{W}_{m}u}}\) via \({{X(\Omega _{1})}}\) | \({{\mathcal{W}_{m}u}}\) via \({{X(\Omega _{2})}}\) | \({{\mathcal{M}u}}\), \(a=3=p^{*}=3\) |
|---|---|---|---|---|
0.0 | 1.00000 | 1.00000 | 1.00000 | 1.00004 |
0.1 | 1.10527 | 1.10518 | 1.10527 | 1.10520 |
0.2 | 1.22140 | 1.22197 | 1.22206 | 1.22213 |
0.3 | 1.34986 | 1.35209 | 1.35215 | 1.35231 |
0.4 | 1.49182 | 1.49742 | 1.49750 | 1.49776 |
0.5 | 1.64872 | 1.66006 | 1.66024 | 1.66340 |
0.6 | 1.82212 | 1.84239 | 1.84268 | 1.84379 |
0.7 | 2.01375 | 2.04696 | 2.04731 | 2.04738 |
0.8 | 2.22554 | 2.27643 | 2.27683 | 2.27759 |
0.9 | 2.45960 | 2.53365 | 2.53415 | 2.53649 |
1.0 | 2.71828 | 2.84435 | 2.84432 | 2.84543 |