edo1D.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Equação que se busca aproximar: y' = 2y com y(0) = 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd \n",
    "import numpy as np \n",
    "import math\n",
    "import plotly.graph_objects as go\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [],
   "source": [
    "index = [0]\n",
    "real_value = [1]\n",
    "aproximated_value = [1]\n",
    "valor_init = 1\n",
    "\n",
    "\n",
    "for i in range(1,100):\n",
    "    index.append(i*0.01)\n",
    "    real_value.append( (1*math.e) ** (2*i*0.01))\n",
    "\n",
    "i = 0\n",
    "\n",
    "def euler_recursivo(i,valor_ant):\n",
    "    if i == 99:\n",
    "        pass\n",
    "    else:\n",
    "        valor_atual = valor_ant + 0.01*2*valor_ant\n",
    "        aproximated_value.append(valor_atual)\n",
    "        euler_recursivo(i+1,valor_atual)\n",
    "\n",
    "euler_recursivo(0,valor_init)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.DataFrame({'index':index,'real_value':real_value,'aproximated_value':aproximated_value})\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "df['error'] = df['real_value'] - df['aproximated_value']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>index</th>\n",
       "      <th>real_value</th>\n",
       "      <th>aproximated_value</th>\n",
       "      <th>error</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.00</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.01</td>\n",
       "      <td>1.020201</td>\n",
       "      <td>1.020000</td>\n",
       "      <td>0.000201</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.02</td>\n",
       "      <td>1.040811</td>\n",
       "      <td>1.040400</td>\n",
       "      <td>0.000411</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.03</td>\n",
       "      <td>1.061837</td>\n",
       "      <td>1.061208</td>\n",
       "      <td>0.000629</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.04</td>\n",
       "      <td>1.083287</td>\n",
       "      <td>1.082432</td>\n",
       "      <td>0.000855</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>95</th>\n",
       "      <td>0.95</td>\n",
       "      <td>6.685894</td>\n",
       "      <td>6.561699</td>\n",
       "      <td>0.124195</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>96</th>\n",
       "      <td>0.96</td>\n",
       "      <td>6.820958</td>\n",
       "      <td>6.692933</td>\n",
       "      <td>0.128025</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>97</th>\n",
       "      <td>0.97</td>\n",
       "      <td>6.958751</td>\n",
       "      <td>6.826792</td>\n",
       "      <td>0.131959</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>98</th>\n",
       "      <td>0.98</td>\n",
       "      <td>7.099327</td>\n",
       "      <td>6.963328</td>\n",
       "      <td>0.135999</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99</th>\n",
       "      <td>0.99</td>\n",
       "      <td>7.242743</td>\n",
       "      <td>7.102594</td>\n",
       "      <td>0.140149</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>100 rows × 4 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "    index  real_value  aproximated_value     error\n",
       "0    0.00    1.000000           1.000000  0.000000\n",
       "1    0.01    1.020201           1.020000  0.000201\n",
       "2    0.02    1.040811           1.040400  0.000411\n",
       "3    0.03    1.061837           1.061208  0.000629\n",
       "4    0.04    1.083287           1.082432  0.000855\n",
       "..    ...         ...                ...       ...\n",
       "95   0.95    6.685894           6.561699  0.124195\n",
       "96   0.96    6.820958           6.692933  0.128025\n",
       "97   0.97    6.958751           6.826792  0.131959\n",
       "98   0.98    7.099327           6.963328  0.135999\n",
       "99   0.99    7.242743           7.102594  0.140149\n",
       "\n",
       "[100 rows x 4 columns]"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head(100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
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            "gridcolor": "white",
            "linecolor": "white",
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   "source": [
    "fig = go.Figure()\n",
    "fig.add_trace(go.Scatter(x=index, y=df['real_value'], mode='lines', name='real_value'))\n",
    "fig.add_trace(go.Scatter(x=index, y=df['aproximated_value'], mode='lines', name='approximated_value'))\n",
    "fig.add_trace(go.Scatter(x=index, y=df['error'], mode='lines', name='error'))\n",
    "\n",
    "# Customize layout\n",
    "fig.update_layout(title='Two Variables Line Plot',\n",
    "                  xaxis_title='X Axis Label',\n",
    "                  yaxis_title='Y Axis Label')\n",
    "\n",
    "# Show plot\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
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           "ticks": "",
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        },
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    "fig = go.Figure()\n",
    "fig.add_trace(go.Scatter(x=index, y=df['real_value'], mode='lines', name='real_value'))\n",
    "fig.add_trace(go.Scatter(x=index, y=df['aproximated_value'], mode='lines', name='approximated_value'))\n",
    "fig.add_trace(go.Scatter(x=index, y=df['error'], mode='lines', name='error'))\n",
    "\n",
    "# Customize layout\n",
    "fig.update_layout(title='Two Variables Line Plot',\n",
    "                  xaxis_title='X Axis Label',\n",
    "                  yaxis_title='Y Axis Label')\n",
    "\n",
    "# Show plot\n",
    "fig.show()"
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