158 lines
22 KiB
Plaintext
158 lines
22 KiB
Plaintext
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{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 10,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"image/png": "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"text/plain": [
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"<Figure size 432x288 with 1 Axes>"
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]
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},
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"metadata": {
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"needs_background": "light"
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},
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"output_type": "display_data"
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}
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],
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"source": [
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"import numpy as np\n",
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"import matplotlib.pyplot as plt\n",
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"import math\n",
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"\n",
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"#We solve the same problem as before\n",
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"\n",
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"\n",
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"\n",
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"t0 = 0\n",
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"tf = 1\n",
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"N = 5\n",
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"\n",
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"t = np.linspace(t0,tf,N)\n",
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"y = np.zeros(N)\n",
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"z = np.zeros(N)\n",
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"w = np.zeros(N)\n",
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"h = (tf-t0)/N\n",
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"\n",
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"y[0] = 1\n",
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"\n",
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"for i in range(0,N-1):\n",
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" y[i+1] = y[i]/(1-h)\n",
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"\n",
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"w = np.exp(t)\n",
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"z = abs(y-w)\n",
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"\n",
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"plt.plot(t,y, label = \"y - Numerical Method method\") #very simple plot of y,z,w\n",
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"plt.plot(t,w,label = \"w - Actual\")\n",
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"plt.plot(t,z,label = \"z - Error\")\n",
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"plt.title(\"Method with N=%d\"%N)\n",
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"plt.legend()\n",
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"plt.show()\n",
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"\n",
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"\n",
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" \n",
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"\n",
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"\n",
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"\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 31,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"array([0. , 0.25, 0.5 , 0.75, 1. ])"
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]
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},
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"execution_count": 31,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"t"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 33,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"0.0\n",
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"0.25\n",
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"0.5\n",
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"0.75\n",
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"1.0\n"
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]
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}
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],
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"source": [
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"for i in t:\n",
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" print(i)\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 39,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"array([0.25, 0.5 , 0.75, 1. ])"
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]
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},
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"execution_count": 39,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"t[1:]"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": []
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}
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],
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"metadata": {
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"interpreter": {
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"hash": "7e1998ff7f8aa20ada591c520b972326324e5ea05489af9e422744c7c09f6dad"
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},
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"kernelspec": {
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"display_name": "Python 3.10.1 64-bit",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.9.10"
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},
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"orig_nbformat": 4
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},
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"nbformat": 4,
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"nbformat_minor": 2
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}
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