Theory and Modern Applications
Table 2 Legendre polynomials and exact solution at different values of variable with absolute error
s | Legendre polynomials | Exact solution | Absolute error |
|---|---|---|---|
0.0 | 0.000002 | 0.000000 | 2.0000 × 10−6 |
0.1 | 0.001005 | 0.001000 | 5.0000 × 10−6 |
0.2 | 0.008004 | 0.008000 | 4.0000 × 10−6 |
0.3 | 0.027011 | 0.027000 | 1.1000 × 10−5 |
0.4 | 0.064010 | 0.064000 | 1.0000 × 10−5 |
0.5 | 0.125012 | 0.125000 | 1.2000 × 10−5 |
0.6 | 0.216003 | 0.216000 | 3.0000 × 10−6 |
0.7 | 0.343011 | 0.343000 | 1.1000 × 10−5 |
0.8 | 0.512003 | 0.512000 | 3.0000 × 10−6 |
0.9 | 0.729010 | 0.729000 | 1.0000 × 10−5 |
1.0 | 1.000012 | 1.000000 | 1.2000 × 10−5 |