x-value | Exact solution | Picard’s solution | Taylor’s solution | Absolute Error (Picard) | Absolute Error (Taylor) |
0 | 1.0000 | 1.0000 | 1.0000 | 0.0000 | 0.0000 |
0.2000 | 0.6407 | 0.6708 | 0.6707 | 0.0301 | 0.0300 |
0.4000 | 0.3348 | 0.4572 | 0.4548 | 0.1224 | 0.1200 |
0.6000 | 0.0571 | 0.3444 | 0.3270 | 0.2873 | 0.2699 |
0.8000 | −0.2014 | 0.3478 | 0.2774 | 0.5492 | 0.4788 |
1.0000 | −0.4389 | 0.5119 | 0.3040 | 0.9508 | 0.7429 |
1.2000 | −0.6463 | 0.9104 | 0.4042 | 1.5567 | 1.0505 |
1.4000 | −0.8094 | 1.6458 | 0.5629 | 2.4551 | 1.3723 |
1.6000 | −0.9110 | 2.8690 | 0.7345 | 3.7599 | 1.6455 |
1.8000 | −0.9314 | 4.6794 | 0.8175 | 5.6109 | 1.7490 |
2.0000 | −0.8498 | 7.3238 | 0.6190 | 8.1736 | 1.4689 |