Theory and Modern Applications
Table 4 The numerical results for Example 4 with \({x}=0.5\), \({M} =2\), \({N} =3\)
r | Exact solution \(( \underline{u} ( x,r ), \overline{u} ( x,r ) )\) | Presented method | Absolute error |
|---|---|---|---|
0 | (0.00000,0.50000) | (0.00000,1.00000) | (3.98881e − 12,4.90985e − 12) |
0.1 | (0.02500,0.47500) | (0.05000,0.95000) | (3.11232e − 12,3.77101e − 12) |
0.2 | (0.05000,0.45000) | (0.10000,0.90000) | (2.34518e − 12,2.77027e − 12) |
0.3 | (0.07500,0.42500) | (0.15000,0.85000) | (1.68740e − 12,1.90765e − 12) |
0.4 | (0.10000,0.40000) | (0.20000,0.80000) | (1.13896e − 12,1.18320e − 12) |
0.5 | (0.12500,0.37500) | (0.25000,0.75000) | (7.67386e − 13,0.00000e + 00) |
0.6 | (0.15000,0.35000) | (0.30000,0.70000) | (4.40253e − 13,1.54612e − 12) |
0.7 | (0.17500,0.32500) | (0.35000,0.65000) | (2.20562e − 13,3.09229e − 12) |
0.8 | (0.20000,0.30000) | (0.40000,0.60000) | (1.08286e − 13,4.63841e − 12) |
0.9 | (0.22500,0.27500) | (0.45000,0.55000) | (1.13459e − 12,1.43827e − 10) |