DescriptionGoursat problem.svg	English: Matplotlib # goursat_triangle_diagram.py import numpy as np import matplotlib.pyplot as plt from matplotlib.patches import Polygon fig, ax = plt.subplots(figsize=(5, 5)) # Axes and limits ax.set_xlim(-0.05, 1.05) ax.set_ylim(-0.05, 1.05) ax.set_aspect('equal', adjustable='box') ax.set_xlabel(r'$x ) ax.set_ylabel(r'$y ) Domain Omega (closure for illustration): triangle with vertices (0,1)-(1,1)-(0,0) tri = np.array([[0, 1], [1, 1], [0, 0]]) patch = Polygon(tri, closed=True, facecolor='0.92', edgecolor='black', linewidth=1.5) ax.add_patch(patch) Characteristic line y = x ax.plot([0, 1], [0, 1], linestyle='--', color='black', linewidth=1) Side labels for boundary data ax.annotate(r'$\phi(t)
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, xy=(0, 0.5), xytext=(-0.12, 0.8),

           ha='right', va='center', rotation=90)

ax.annotate(r'$\psi(t)}}, xy=(0.5, 1), xytext=(0.5, 1.08),

           ha='center', va='bottom')

1. Parameter guides

ax.annotate(r'$t\in[0,1]}}, xy=(0, 0.15), xytext=(-0.18, 0.15),

           ha='right', va='center', rotation=90)

ax.annotate(r'$t\in[0,1]}}, xy=(0.15, 1), xytext=(0.15, 1.08),

           ha='center', va='bottom')

1. Label the domain

ax.text(0.25, 0.75, r'$\Omega:\ 0<x<y<1}}, ha='center', va='center')

1. Ticks and frame

ax.set_xticks([0, 1]) ax.set_yticks([0, 1]) ax.set_xticklabels(['0', '1']) ax.set_yticklabels(['0', '1']) ax.spines'right', 'top'.set_visible(False)

plt.tight_layout() plt.savefig('Goursat problem.svg') plt.show() }}}} |date=2025-09-29 |source=Own work |author=Cosmia Nebula }}

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