Euler's Method.ipynb

Kernel: Python 3 (system-wide)

Euler's Method

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

@njit
def fprime(x):
    return np.cos(x)

@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)

fig, ax = plt.subplots(figsize=(20,20))

X_0,Y_0 = EMethod(0,10,1,0)
X_1,Y_1 = EMethod(0,10,.5,0)
X_2,Y_2 = EMethod(0,10,.1,0)
X_3,Y_3 = EMethod(0,10,.00001,0)

ax.plot(X_0,Y_0,'.', ms=10);
ax.plot(X_1,Y_1,'.', ms=5);
ax.plot(X_2,Y_2,'.', ms=3);
ax.plot(X_3,Y_3,'.',  ms=1);


X = np.arange(0,10,.001)
Y = np.array([np.sin(x) for x in X])
ax.plot(X,Y);