Function printVdpol

Example

// TypeScript usage example
import {printVdpol} from 'diff-grok';

printVdpol();
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# Python reference calculation for comparison
import numpy as np
import pandas as pd
from scipy.integrate import solve_ivp

# -------------------------
# 0. Solver method
# -------------------------
METHOD = "Radau"  # stiff solver recommended for van der Pol with large mu

# -------------------------
# 1. Define van der Pol ODE (stiff)
# -------------------------
def vdpol(t, y):
   x1, x2 = y
   dx1 = x2
   dx2 = -x1 + 1000 * (1 - x1**2) * x2  # mu = 1000
   return [dx1, dx2]

# -------------------------
# 2. Initial conditions and time
# -------------------------
y0 = [-1, 1]
t_start = 0.0
t_end = 2000.0
t_step = 0.1

# Use linspace to avoid "t_eval not in t_span" error
n_points = int(np.ceil((t_end - t_start) / t_step)) + 1
t_eval = np.linspace(t_start, t_end, n_points)

# -------------------------
# 3. Solve ODE
# -------------------------
sol = solve_ivp(
   vdpol,
   (t_start, t_end),
   y0,
   method=METHOD,
   t_eval=t_eval,
   rtol=1e-12,
   atol=1e-12
)

print("Success:", sol.success)
print("Message:", sol.message)

# -------------------------
# 4. Save solution to CSV
# -------------------------
data = np.column_stack((sol.t, sol.y.T))
col_names = ['t', 'x1', 'x2']

df = pd.DataFrame(data, columns=col_names)
filename = f"VANDERPOL-using-{METHOD}.csv"
df.to_csv(filename, index=False)

print(f"Solution saved to '{filename}'")

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