h (step size)

for the exact solution

for Heun’s method

Error on Heun’s

Error on Euler [12]

Error on Runge Kutta [12]

0.25

1318.179242

1306.250000

11.929242

68.179242

156.820758

0.125

1140.431227

1128.515625

1.368727

15.431227

97.068773

0.025

1025.572765

1025.562500

0.010265

0.572765

21.927235

0.0025

1002.505635

1002.505625

0.000010

0.005635

2.244365

0.25

1306.122449

1296.875000

9.247449

56.122449

131.377551

0.125

1137.777778

1136.718750

1.059028

12.777778

80.972222

0.025

1025.572765

1025.468750

0.007936

0.476686

18.273314

0.0025

1002.505635

1002.504688

0.000007

0.004695

1.870305

0.25

1764.823762

1687.500000

77.323762

264.823762

485.176238

0.125

1305.122500

1296.875000

8.247500

55.122500

319.877500

0.025

1051.933860

1051.875000

0.058860

1.933860

73.066140

0.0025

1005.018808

1005.018750

0.000058

0.018808

7.481192