Table 3 Approximate solutions with \(m=5\) in [5] for Example 1
|  | Method in [5] with m = 5 | Exact solution | ||
|---|---|---|---|---|
x | \(y_{1}\) | \(y_{2}\) | \(y_{1}(x)\) | \(y_{2}(x)\) |
0.0 | 2.3 × 10−13 | 1 | 0 | 1 |
0.1 | – | – | 0.099833417 | 0.995004165 |
0.2 | 0.198669 | 0.980066 | 0.198669331 | 0.980066578 |
0.3 | – | – | 0.295520207 | 0.955336489 |
0.4 | 0.389419 | 0.92106 | 0.389418342 | 0.921060994 |
0.5 | – | – | 0.479425539 | 0.877582562 |
0.6 | 0.564646 | 0.825337 | 0.564642473 | 0.825335615 |
0.7 | – | – | 0.644217687 | 0.764842187 |
0.8 | 0.717369 | 0.696719 | 0.717356091 | 0.696706709 |
0.9 | – | – | 0.783326910 | 0.621609968 |
1.0 | 0.841529 | 0.540404 | 0.841470985 | 0.540302306 |