File:Stability region for Euler method.svg

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Original file (SVG file, nominally 720 × 540 pixels, file size: 23 KB)

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Description
English: Stability region for Euler method
Date
Source Own work
Author Helmut Podhaisky
Other versions Euler method -- Trapzoidal method -- Adams Bashforth
SVG development
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This plot was created with Matplotlib.
Source code
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Python code

from pylab import linspace,pi,exp,real,imag,axis

import matplotlib.path as mpath
import matplotlib.patches as mpatches
import matplotlib.pyplot as plt

w=exp(1j*linspace(0,2*pi,200))

Path=mpath.Path
fig = plt.figure()

for name,z in zip(['Euler','trapezoidal',  'AB2'],\
                  [ w-1,       [5j,-5 5j,-5-5j,-5j,5j],2*(w**2-w)/(3*w-1)]):
    fig.clf()
    ax=fig.add_subplot(111)

    verts=map(lambda z:(real(z),imag(z)), z)
    codes=[Path.MOVETO] [Path.LINETO]*(len(verts)-2) [Path.CLOSEPOLY]

    path=mpath.Path(verts,codes)
    patch=mpatches.PathPatch(path,facecolor=[1, 0.5, 0.8],edgecolor='black',alpha=1)
    ax.add_patch(patch)
    ax.plot([-3,2],[0,0],'--',color='black')
    ax.plot([0,0],[-2,2],'--',color='black')
    ax.set_xlim(-3,2)
    ax.set_ylim(-2,2)

    fig.savefig("Stability region for " name " method.svg")

Licensing

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Public domain I, the copyright holder of this work, release this work into the public domain. This applies worldwide.
In some countries this may not be legally possible; if so:
I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.

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Date/TimeThumbnailDimensionsUserComment
current09:46, 26 August 2010Thumbnail for version as of 09:46, 26 August 2010720 × 540 (23 KB)Helmut.podhaisky (talk | contribs)no
09:24, 26 August 2010Thumbnail for version as of 09:24, 26 August 2010720 × 540 (23 KB)Helmut.podhaisky (talk | contribs){{Information |Description={{en|1=Stability region for Euler method}} |Source=python script |Author=Helmut Podhaisky |Date=2010-08-26 |Permission= |other_versions= }}

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