File:Shooting method trajectories.svg

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Summary

Description
English: Graph showing trajectories of the shooting method for different values of the initial value of w'(0).
Español: Gráfico que muestra trayectorias del método de disparo para diferentes valores del valor inicial para w'(0).
Date
Source Own work
Author Nicoguaro
SVG development
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Source code
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Python code

# -*- coding: utf-8 -*-
"""
Illustrate the shooting method for the equation

    w'' = 3/2*w**2

The initial values picked for the first derivative are
w'(0) = s = [-40, -36, -10, -8, -7]
"""
from __future__ import division
import numpy as np
import matplotlib.pyplot as plt
from scipy.integrate import odeint
import seaborn as sns

sns.set_style("white")


def func(y, t):
    return [y[1], 1.5*y[0]**2]


t = np.linspace(0, 1.1, 50)
diff_ini = [-40, -36, -10, -8, -7]
plt.figure(figsize=(6, 4))
for dy in diff_ini:
    y0 = [4, dy]    
    y = odeint(func, y0, t)
    plt.plot(t, y[:, 0], label=r"$s=%i$" % dy)

plt.plot(1, 1, "o", mfc="#3c3c3c")
plt.legend(loc="best")
plt.xlabel(r"$t$")
plt.ylabel(r"$w(t; s)$")
plt.savefig("Shooting_method_trajectories.svg", bbox_inches="tight")
plt.show()

Licensing

I, the copyright holder of this work, hereby publish it under the following license:
w:en:Creative Commons
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9 November 2016

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Date/TimeThumbnailDimensionsUserComment
current00:07, 10 November 2016Thumbnail for version as of 00:07, 10 November 2016495 × 350 (45 KB)NicoguaroUser created page with UploadWizard

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