euler_tut.py

Created by vnap0v

Created on August 12, 2025

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Euler’s method using Python

On the English YouTube channel of Numworks, there is a tutorial on using the sequences app to apply Euler’s method on a differential equation:

Euler’s method using sequences

This script does the same calculations, using Python instead.

The differential equation:

dy/dx = sqrt(x) * y
y(1) = 4

For Euler’s method step h=0.25

Tested on the Numworks calculator using software version 24.3.0

# Python version of Euler's method
# originally using the sequence app
# in Numworks tutorial
# https://youtu.be/JIc2p6jtGhs?si=QwTqrjLIRexZK6hJ
from math import *
# parameters
h=0.25 # x step
x_init=1 # initial values
y_init=4
n_iter=8 # number of steps

# function defines differential
# equation by returning value
# of derivative of y
def dy_dx(x,y):
    value_dy_dx=sqrt(x)*y
    return value_dy_dx

x=x_init # start with initial values
y=y_init
print("{0:<6} {1:<10}".format("x","y"))
print("-"*10)
for _ in range(n_iter):
    print("{0:<6} {1:<10.10f}".format(x,y))
    # calculate new y value using Euler
    y+=dy_dx(x,y) * h
    x+=h