{"nbformat":4,"nbformat_minor":0,"metadata":{"anaconda-cloud":{},"kernelspec":{"display_name":"Python [default]","language":"python","name":"python3"},"language_info":{"codemirror_mode":{"name":"ipython","version":3},"file_extension":".py","mimetype":"text/x-python","name":"python","nbconvert_exporter":"python","pygments_lexer":"ipython3","version":"3.5.2"},"toc":{"base_numbering":1,"nav_menu":{},"number_sections":true,"sideBar":true,"skip_h1_title":false,"title_cell":"Table of Contents","title_sidebar":"Contents","toc_cell":false,"toc_position":{},"toc_section_display":true,"toc_window_display":false},"colab":{"name":"mac0209-movimento-1D-exercicios-vazia.ipynb","provenance":[]}},"cells":[{"cell_type":"markdown","metadata":{"id":"BIh1Jolrd73p","colab_type":"text"},"source":["<font size=\"5\"> <a href=\"https://uspdigital.usp.br/jupiterweb/obterDisciplina?sgldis=MAC0209\"> MAC0209 - Modelagem e Simulação</a> </font>\n","\n","Roberto M. Cesar Jr. (IME-USP)\n","\n","Roberto Hirata Jr. (IME-USP)\n","***\n","<font size=\"5\"> Resoluções de EDOs: soluções analítica e numérica pelo método de Euler </font>\n","***"]},{"cell_type":"markdown","metadata":{"id":"3B2NDLdpd73s","colab_type":"text"},"source":["# Método de Euler para solução de EDOs"]},{"cell_type":"markdown","metadata":{"id":"0LRRQDPCd73t","colab_type":"text"},"source":["O método de Euler é uma forma de resolver numericamente uma equação diferencial ordinária. Assume-se ser conhecidas a derivada de uma função que se quer encontrar (\"resolver\") e um valor inicial da equação a ser integrada. Por exemplo, no caso do movimento uniformemente acelerado:$$a=\\mbox{constante}, b=\\mbox{constante}$$\n","\n","$$v(t) = x'(t) = \\frac{dx(t)}{dt} = 2at + b$$, $$x(0)=0$$\n","\n","A ideia do método de Euler é substituir a derivada por uma aproximação de Taylor, desprezando-se os termos maiores que segunda ordem. Isto é:\n","\n","$$x'(t)\\sim \\frac{x(t+\\Delta t)-x(t)}{\\Delta t}$$\n","\n","Se denotarmos os valores de $x(t)$ por $x_t$, isto é, ao invés da notação de função, usarmos a notação com índices, e assumirmos que os valores de $t$ só podem ser números inteiros (portanto $\\Delta t$ é no mínimo 1, o valor $x(t+\\Delta t)$ pode ser escrito como $x_1$, para $t=0$; $x_2$, para $t=1$ e assim por diante. \n","\n","Desta maneira, o exemplo poderia ser escrito assim (note que já estamos assumindo $\\Delta t = 1$:\n","\n","$$v(t) = x'(t) = 2*a*t + b \\sim x_t - x_{t-1},$$\n","\n","isto é,\n","\n","$$ x_t = x_{t-1} + 2*a*t + b $$\n","\n","Como sabemos o valor inicial em $t=0$, podemos calcular $x_t$ para todo $t>0$:\n","\n","$$ x_1 = x_{0} + 2*a*1 + b $$\n","\n","$$ x_2 = x_{1} + 2*a*2 + b = 6*a + 2*b$$\n","\n","$$ x_3 = x_{2} + 2*a*3 + b = 6*a + 2*b + 6*a + b = 12*a + 3*b$$\n","\n","e assim por diante.\n","\n","Em verdade, $\\Delta t$ não precisa ser um número inteiro e em geral, não é. Porém, no caso de não ser um número inteiro, desacoplamos os índices do incremento pois os índices são inteiros. \n","\n"]},{"cell_type":"markdown","metadata":{"id":"8ZUq92S9d73u","colab_type":"text"},"source":["# Implementanto o método de Euler"]},{"cell_type":"markdown","metadata":{"id":"nXEMFyX2d73v","colab_type":"text"},"source":["Da forma que a equação foi construída, isto é, $ x_t = x_{t-1} + 2*a*t + b $, é trivial implementá-la. basta que estabeleçamos os valores de $a$, $b$ e $x_0$.\n","\n","No entanto, para a implementação ficar organizada, crie duas funções: \n","- nextXeuler(x,t,params,dt): que recebe um vetor de parâmetros iniciais, params, o tempo e a posição atual, t e x, respectivamente, e o delta de tempo, dt (note que com isso desacoplamos os índices do incremento). A função retorna a nova posição $x_t$ de acordo com o método de Euler: $ x_t = x_{t-1} + 2*a*t + b $ .\n","- nextXa(t,params): que recebe um vetor de parâmetros iniciais, params, e o tempo atual. A função retorna a nova posição $x_t$ de acordo com a equação integrada analiticamente: $ x_t = a*t^2 + b*t + x_0 $.\n","\n","Crie uma função main que itera essas duas funções entre os tempos 0s e 2s (com um dt de 0.1s) calcula e imprime a diferença entre elas (erro) e as grafique.\n"]},{"cell_type":"code","metadata":{"id":"Y4DOZKj-d73w","colab_type":"code","outputId":"73c42acd-147e-4245-9451-d1f569542c20","colab":{}},"source":["# Implementa o exercício da integração de Euler de dx(t)/dt = 2at + b\n","\n","import math\n","import matplotlib.pyplot as pyplot\n","\n","def nextXeuler(x,t,params,dt):\n","   \n","\n","def nextXa(t,params):\n","\n","def main():\n"],"execution_count":0,"outputs":[{"output_type":"stream","text":["Erro:  0\n","Erro:  0.009999999999999981\n","Erro:  0.01999999999999999\n","Erro:  0.02999999999999997\n","Erro:  0.040000000000000036\n","Erro:  0.050000000000000044\n","Erro:  0.06000000000000005\n","Erro:  0.07000000000000006\n","Erro:  0.08000000000000007\n","Erro:  0.0900000000000003\n","Erro:  0.10000000000000053\n","Erro:  0.11000000000000032\n","Erro:  0.1200000000000001\n","Erro:  0.12999999999999945\n","Erro:  0.13999999999999924\n","Erro:  0.14999999999999858\n","Erro:  0.15999999999999837\n","Erro:  0.16999999999999815\n","Erro:  0.17999999999999794\n","Erro:  0.18999999999999773\n"],"name":"stdout"},{"output_type":"display_data","data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAAW4AAAEICAYAAAB/Dx7IAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRNLM/wNJJMk8gJhcYwAAAABJRU5ErkJggg==\n","text/plain":["<matplotlib.figure.Figure at 0x10654fdd8>"]},"metadata":{"tags":[]}}]},{"cell_type":"markdown","metadata":{"id":"mzxTwHdZd731","colab_type":"text"},"source":["# Exercício: $\\frac{d^2x}{dt^2} = 6t$"]},{"cell_type":"markdown","metadata":{"id":"-nIZu_zud732","colab_type":"text"},"source":["Escreva a solução para a EDO:\n","\n","$ \\frac{d^2x}{dt^2} = 6t$\n","\n"]},{"cell_type":"code","metadata":{"id":"Pchrbkkod733","colab_type":"code","colab":{}},"source":["# Escreva sua solucao aqui."],"execution_count":0,"outputs":[]},{"cell_type":"markdown","metadata":{"id":"s08TE6Gfd739","colab_type":"text"},"source":["Depois de ter escrito sua solução, compare com a resolução abaixo:\n"]},{"cell_type":"code","metadata":{"code_folding":[0],"id":"-D58Ca6od73-","colab_type":"code","outputId":"bfa8a930-ce17-4ee4-dcb2-439df5289eef","colab":{}},"source":["# d2x / dt2 = 6t\n","\n"],"execution_count":0,"outputs":[{"output_type":"stream","text":["Erro:  0\n","Erro:  0.005000000000000002\n","Erro:  0.016000000000000007\n","Erro:  0.033\n","Erro:  0.05600000000000001\n","Erro:  0.08500000000000005\n","Erro:  0.1200000000000001\n","Erro:  0.1610000000000002\n","Erro:  0.2080000000000003\n","Erro:  0.26100000000000045\n","Erro:  0.3200000000000006\n"],"name":"stdout"},{"output_type":"display_data","data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAAXcAAAEICAYAAACktLTqAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nJJDCXUQkgRTuIiIJpHAXEUmg/weyqrBn4P0QNAAAAABJRU5ErkJggg==\n","text/plain":["<matplotlib.figure.Figure at 0x118573860>"]},"metadata":{"tags":[]}},{"output_type":"display_data","data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAAXcAAAEICAYAAACktLTqAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\npgheMvjWVk8AAAAASUVORK5CYII=\n","text/plain":["<matplotlib.figure.Figure at 0x104e6c940>"]},"metadata":{"tags":[]}}]},{"cell_type":"code","metadata":{"id":"cFTrL_QEd74B","colab_type":"code","colab":{}},"source":[""],"execution_count":0,"outputs":[]}]}