CoCalc -- Euler's Method.ipynb

Path: 2.2/Physics 255/Euler's Method.ipynb

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Kernel: Python 3 (Ubuntu Linux)

Euler's Method

In [4]:

import numpy as np
from numba import njit
import matplotlib.pyplot as plt
from matplotlib import collections as mc

In [2]:

@njit
def fprime(x):
    return np.cos(x)*x**(1/2)

@njit
def EMethod(xstart, xend, deltax, ystart):
    outputX = np.arange(xstart,xend+deltax,deltax)
    outputY = np.array([ystart]*len(outputX), dtype = np.float64)
    for i in range(1,len(outputX)):
        outputY[i] = outputY[i-1] + fprime(outputX[i])*deltax
    return (outputX,outputY)

In [5]:

fig, ax = plt.subplots(figsize=(10,10))

X_1,Y_1 = EMethod(0,10,.5,4)
X_2,Y_2 = EMethod(0,10,.1,4)
X_3,Y_3 = EMethod(0,10,.001,4)

ax.plot(X_1,Y_1,'.', ms=5);
ax.plot(X_2,Y_2,'.', ms=3);
ax.plot(X_3,Y_3,'.', ms=1);