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File:Singular perturbation convergence.svg

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Summary

Description
English: A demonstration of convergence of singular perturbation solutions. Shows solutions to

with , , for varying .

Created with the following Sage code:

var('t')
var('eps')
y(t) = (exp(-t) - exp(-t/eps))/(exp(-1) - exp(-1/eps))
yO(t) = exp(1 - t)
combined = plot(y.subs(eps=0.1), t, 0, 1, color='red', legend_label='$\epsilon=0.1$') + plot(y.subs(eps=0.07), t, 0, 1, color='green', legend_label='$\epsilon=0.07$') + plot(y.subs(eps=0.04), t, 0, 1, color='blue', legend_label='$\epsilon=0.04$') + plot(y.subs(eps=0.01), t, 0, 1, color='magenta', legend_label='$\epsilon=0.01$') + plot(yO, t, 0, 1, color='black', legend_label='$y_O$')
combined.set_legend_options(shadow=False)
combined.show(ymax=3, axes_labels=['$t$', ''])
Date
Source Own work
Author Eviatar Bach
 
This diagram was created with SageMath.

Licensing

I, the copyright holder of this work, hereby publish it under the following license:
Creative Commons CC-Zero This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication.
The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.

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5 November 2016

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Date/TimeThumbnailDimensionsUserComment
current22:46, 5 November 2016Thumbnail for version as of 22:46, 5 November 2016701 × 525 (44 KB)InverseHypercubeUser created page with UploadWizard

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