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