Numerical continuation of nonlinear equilibrium equations
Project description
contique
Numeric continuation of equilibrium equations
Example
A given set of equilibrium equations in terms of x and lpf (a.k.a. load-proportionality-factor) should be solved by numeric continuation of a given initial solution.
Function definition
def fun(x, lpf, a, b):
return np.array([-a * np.sin(x[0]) + x[1]**2 + lpf,
-b * np.cos(x[1]) * x[1] + lpf])
with it's initial solution
x0 = np.zeros(2)
lpf0 = 0.0
and function parameters
a = 1
b = 1
Run contique.solve and plot equilibrium states
Res = contique.solve(
fun=fun,
x0=x0,
args=(a, b),
lpf0=lpf0,
dxmax=0.05,
dlpfmax=0.05,
maxsteps=80,
maxcycles=4,
maxiter=20,
tol=1e-6,
)
Assemble results
X = np.array([res.x for res in Res])
and plot the solution curve.
import matplotlib.pyplot as plt
plt.plot(X[:, 0], X[:, 1], ".-")
plt.xlabel('$x_1$')
plt.ylabel('$x_2$')
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