# # Stability regions for Taylor's methods # Vincent Legat - 2018 # Ecole Polytechnique de Louvain # import matplotlib.pyplot as plt from numpy import * from math import factorial x,y = meshgrid(linspace(-4,4,1000),linspace(-3,3,1000)) z = x + 1j*y plt.figure("Stability of Taylor's Methods ") for n in [4,3,2,1]: f = ones(shape(z)) for m in range(n,0,-1): f = f + z**m/factorial(m) f = abs(f) plt.contourf(x,y,f,[0,1,100],colors=('lightgreen','none')) plt.contour(x,y,f,[1],colors='black',linewidths=0.5) ax = plt.gca() ax.axhline(y=0,color='gray',linewidth=0.5) ax.axvline(x=0,color='gray',linewidth=0.5) #ax.yaxis.grid(color='gray',linestyle='dashed') #ax.xaxis.grid(color='gray',linestyle='dashed') plt.xticks(arange(-3,4,1)) plt.yticks(arange(-3,4,1)) plt.axis('equal') plt.show()