dissertation_work/Programming/Python files/Backward_Euler.ipynb

158 lines
22 KiB
Plaintext

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