Here is what you get with h=0.1 using the Midpoint Method:
Here is what you get with h=0.1 using the Euler's Method:
h | Exact Result | Midpoint Result | Euler Result | Midpoint Error | Euler Error |
0.2 | 3.2190993e+00 | 3.2345605e+00 | 2.3106453e+00 | 1.5461209e-02 | 9.0845401e-01 |
0.1 | 3.2190993e+00 | 3.2254163e+00 | 2.7609015e+00 | 6.3169639e-03 | 4.5819785e-01 |
0.05 | 3.2190993e+00 | 3.2209628e+00 | 2.9897243e+00 | 1.8634692e-03 | 2.2937507e-01 |
0.025 | 3.2190993e+00 | 3.2190993e+00 | 4.9960005e-04 |
Estimate order according to p = log[error(h)/error(h/2)]/log[2]
Euler:
h=0.2/h=0.1: p=0.987
h=0.1/h=0.05: p=0.998
Midpoint:
h=0.2/h=0.1: p=1.291
h=0.1/h=0.05: p=1.761
h=0.05/h=0.025: p=1.900