Figure 2.12:

Leading-order inner U_0, outer u_0, and composite solutions u_{0c}, for Example \ref {ex:rxequil} with \epsilon =0.2, K=1, and k_{2}=1.

Code for Figure 2.12

Text of the GNU GPL.

main.py

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import numpy as np
import matplotlib.pyplot as plt

plt.figure()

K = 1
eps = 2e-1
t = np.arange(0, 2.01, 0.01)
Uinn = np.exp(-(1+K)*t/eps) + 1/(1+K)*(1 - np.exp(-(1+K)*t/eps))
plt.plot(t, Uinn, '--')

Vinn = 1 - Uinn

Uout = 1/(1+K) * np.exp(-K/(1+K)* t)
plt.plot(t, Uout, ':')

Ucomp = Uinn + Uout - Uout[0]
plt.plot(t, Ucomp)

plt.xlabel('t')
plt.ylabel('u(t)')
plt.axis([0, 2, 0, 1])
plt.legend(['Inner solution', 'Outer solution', 'Composite solution'])
plt.show(block=False)

data = np.column_stack( (t, Ucomp, Uinn, Uout) )
with open("rxnequil.dat", "w") as f:
    np.savetxt(f, data, fmt='%f', header="data")