```python
import numpy as np
import sympy as sp
import matplotlib.pyplot as plt
import Euler as p1
import nonlinear_ODE as p2
```

# Exercise C.2 Solving a nonlinear ODE
Solves the ODE problem: $$u^\prime = u^q,\ u(0) = 1,\ t\epsilon [0,T]$$

$q=1,\ \Delta t=0.1:$


```python
p2.graph(1, 0.1, 1)
```

$q=1,\ \Delta t=0.01:$


```python
p2.graph(1, 0.01, 1)
```

$q=2,\ \Delta t=0.1:$


```python
p2.graph(2, 0.1, 1)
```

$q=12,\ \Delta t=0.01:$


```python
p2.graph(2, 0.01, 1)
```

$q=3,\ \Delta t=0.1:$


```python
p2.graph(3, 0.1, 1)
```


```python
p2.graph(3, 0.01, 1)
```

The Euler Method is most accurate for small $\Delta t$, which corresponds to a larger number of calculations, and small $q$.

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temporary_for_nonlinear_ODE.ipynb
chapman-phys227-2016s/cw-6-classwork-team
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temporary_for_nonlinear_ODE.ipynb
chapman-phys227-2016s/cw-6-classwork-team
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temporary_for_nonlinear_ODE.ipynb
chapman-phys227-2016s/cw-6-classwork-team
ab705f3d4c2577eafa3b521cf51bf903c48b1ff6
MIT
Qwen/Qwen-72B
1. YES
2. YES