Theory and Modern Applications
Table 3 The numerical results for Example 3 with \({x}=0.5\), \({M} =2\), \({N} =3\)
r | Exact solution \(( \underline{u} ( x, r ), \overline{u} ( x, r ))\) | Presented method | Absolute error |
|---|---|---|---|
0 | (0.00000,1.00000) | (0.00000,1.00000) | (1.11378e − 11,9.60654e − 12) |
0.1 | (0.05000,0.95000) | (0.05000,0.95000) | (8.82267e − 12,7.71254e − 12) |
0.2 | (0.10000,0.90000) | (0.10000,0.90000) | (6.79151e − 12,5.94123e − 12) |
0.3 | (0.15000,0.85000) | (0.15000,0.85000) | (5.04428e − 12,4.29281e − 12) |
0.4 | (0.20000,0.80000) | (0.20000,0.80000) | (3.58099e − 12,2.76719e − 12) |
0.5 | (0.25000,0.75000) | (0.25000,0.75000) | (1.53477e − 12,0.00000e + 00) |
0.6 | (0.30000,0.70000) | (0.30000,0.70000) | (8.80507e − 13,3.09224e − 12) |
0.7 | (0.35000,0.65000) | (0.35000,0.65000) | (4.41125e − 13,6.18459e − 12) |
0.8 | (0.40000,0.60000) | (0.40000,0.60000) | (2.16571e − 13,9.27682e − 12) |
0.9 | (0.45000,0.55000) | (0.45000,0.55000) | (1.80808e − 11,1.17943e − 10) |