Theory and Modern Applications
Table 1 Legendre polynomials and exact solution at different values of variable with absolute error
s | Legendre polynomials | Exact solution | Absolute error |
|---|---|---|---|
0.0 | 0.000006 | 0.000000 | 6.0000 × 10−6 |
0.1 | 0.121003 | 0.012000 | 1.0300 × 10−4 |
0.2 | 0.055900 | 0.056000 | 1.0000 × 10−5 |
0.3 | 0.144110 | 0.144000 | 1.1000 × 10−4 |
0.4 | 0.287800 | 0.288000 | 2.0000 × 10−4 |
0.5 | 0.500190 | 0.500000 | 1.9000 × 10−4 |
0.6 | 0.800012 | 0.792000 | 0.8000 × 10−5 |
0.7 | 0.176100 | 1.176000 | 1.0000 × 10−4 |
0.8 | 1.664020 | 1.664000 | 2.0000 × 10−5 |
0.9 | 2.267900 | 2.268000 | 1.0000 × 10−4 |
1.0 | 3.000130 | 3.000000 | 1.3000 × 10−4 |