From 633106ede62205f8eaccc0ede0983e1ac9cf430b Mon Sep 17 00:00:00 2001 From: Victor Aguiar Date: Thu, 13 Jun 2019 16:13:32 -0300 Subject: [PATCH] changed --- codes/euler.py | 80 --------------------------------------------- figs/euler_ex1.png | Bin 29833 -> 0 bytes 2 files changed, 80 deletions(-) delete mode 100644 codes/euler.py delete mode 100644 figs/euler_ex1.png diff --git a/codes/euler.py b/codes/euler.py deleted file mode 100644 index 6751440..0000000 --- a/codes/euler.py +++ /dev/null @@ -1,80 +0,0 @@ - -####################################################### -### Programa utilizado para aproximar numericamente ### -### a seguinte ODE: ### -### ### -### dy/dt = 3 + e^(-t) - 1/2*y, y(0) = 1 ### -### ### -### Utilizado o Metodo de Euler: ### -### y[n+1] = y[n] +f(t[n], y[n])*(t[n+1] - t[n]) ### -### ----------------------------------------------- ### -### "Equacoes Diferenciais Elementares e Problemas ### -### de Valores de Contorno" - Boyce & Diprima ### -### 8ยบ Ed. Cap: 2.7, Exemplo: 1 ### -### ----------------------------------------------- ### -####################################################### - -import seaborn as sns -import numpy as np -import matplotlib.pyplot as plt - -sns.set(style="darkgrid") -fig, ax = plt.subplots() - -dt = [0.1, 0.05, 0.025, 0.01] -f0 = 1 # Initial condition -tn = 5 # Size of grid - -for i in dt: - dt = i # Time interval (0.5, 2) --- - N_t = int(tn/dt) # N_t = tn/dt -- Number of meshgrid points - - from numpy import linspace, zeros, exp - t = linspace(0, (N_t)*dt, N_t+1) - y = zeros(N_t+1) - f = zeros(N_t+1) - - y[0] = f0 - - for n in range(N_t): - f[n] = 3 + np.exp(-t[n]) - (1/2)*y[n] - #print(f[n]) - y[n+1] = y[n] + dt*f[n] - - ax.plot(t, y, label = 'dt = %s'%("{0:.3f}".format(i))) - -########################### -### Analytical solution ### -########################### - -ta = np.arange(0, tn+1, 1) -ya = 6 - 2*np.exp(-ta) - 3*np.exp(-ta/2) - -ax.plot(ta, ya, color='lawngreen', label = 'exact') - -plt.yticks(np.arange(0, 7, 1)) -plt.xticks(np.arange(0, 7, 1)) - -##################### -### Legend format ### -##################### - -legend_properties = {'weight':'semibold', -'size':8} - -### Organize labels ### - -leg = ax.legend(loc=2, prop=legend_properties) - -### Set linewdith separately from lines plotted ### -for line in leg.get_lines(): - line.set_alpha(1) - -frame = leg.get_frame() -frame.set_color('gainsboro') - -plt.xlabel('t', size = 12, weight = 'semibold'); -plt.xticks(size = 10, weight = 'semibold') - -plt.ylabel(u'$y(t)$', size = 14, weight = 'semibold') -plt.yticks(size = 10, weight = 'semibold') diff --git a/figs/euler_ex1.png b/figs/euler_ex1.png deleted file mode 100644 index d230b43ac24303c14188657280e094e2e1047945..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 29833 zcmeFYWl)_#*DZK(cY?dSy9aj-5Zv9}CBa=2+yf-I1oxca?(QDk9p>TvzFT+d-kPcT zF+b+Vq>AEja!x!1Q`qhL2SUo0`G87uIvE6 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