dissertation_work/Programming/Python files/eulermethod.ipynb

84 lines
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Plaintext

{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x7fcea17426d0>]"
]
},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
},
{
"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 #import appropriate libraries\n",
"import matplotlib.pyplot as plt\n",
"\n",
"start = 0 #start point of the domain over which the diffeq will be solved\n",
"end = 1 #end-point\n",
"steps = 30 # number of steps\n",
"t = np.linspace(start, end, steps) # t is a uniformly spaced vector spanning the start and endpoints\n",
"y = np.zeros(len(t)) # y is a vector initialized to 0 as long as t\n",
"h = (end - start)/steps # h is the width of each step\n",
"t = t*h # t is h times the number of t's gone before\n",
"\n",
"y[0] = 1 # initial value\n",
"\n",
"for i in range (0,len(t)-1): # initiate loop\n",
" y[i+1] = y[i] + h * (-6*y[i]) # euler method\n",
"plt.plot(t,y) # plot the graph"
]
},
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