x-value

Exact solution

Picard’s solution

Taylor’s solution

Absolute Error (Picard)

Absolute Error

(Taylor)

0

0.0000

0.0000

0.0000

0.0000

0.0000

0.2000

1.7783

1.7783

1.7783

0.0000

0.0000

0.4000

3.2342

3.2342

3.2342

0.0001

0.0001

0.6000

4.4262

4.4267

4.4267

0.0006

0.0006

0.8000

5.4021

5.4053

5.4053

0.0032

0.0032

1.0000

6.2011

6.2130

6.2130

0.0119

0.0119

1.2000

6.8553

6.8899

6.8899

0.0346

0.0346

1.4000

7.3909

7.4761

7.4761

0.0852

0.0852

1.6000

7.8294

7.0146

7.0146

0.1852

0.1852

1.8000

8.1884

8.5549

8.5549

0.3665

0.3665

2.0000

8.4824

9.1560

9.1560

0.6736

0.6736