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"cells": [
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"source": [
"\n",
"\n",
"\n",
"# Simple implementation of Euler's method\n",
"\n",
"## Modules – Basics\n",
"\n",
"By Niels Henrik Aase, Thorvald Ballestad, Eilif Sommer Øyre and Jon Andreas Støvneng\n",
"\n",
"Last edited: November 5th 2019\n",
"\n",
"___\n",
"This notebook serves as a very simple demonstration of Euler's method, the simplest numerical method to solve a first order differential equation. Our sole focus will be on the __implementation__, as we will only provide the most essential theory. For a more thorough notebook on Euler's method, check out our other notebook on *[Euler's method](https://nbviewer.jupyter.org/urls/www.numfys.net/media/notebooks/eulers_method.ipynb)*.\n",
"___"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Introduction\n",
"\n",
"In all kinds of natural sciences, we encounter differential equations. These equations can be quite complicated to solve analytically, and most times there does not exist an analytical solution. Nonetheless, we still need solve these kinds of equations in order for them to better our understanding of whichever underlying physical system we are working with.\n",
"\n",
"For many students, understanding how to solve ordinary differential equations, ODEs for short, can be a time consuming and frustrating process. The purpose of this notebook is to simply demonstrate __how__ an ODE can be solved. Will not focus on the theory behind Euler's method, we will solely focus on the __implementation__ of our ODE solver. Ideally, the reader should also understand the theory and possible pitfalls of using Euler's method, thus we strongly recommend also reading our other module on *[Euler's method](https://nbviewer.jupyter.org/urls/www.numfys.net/media/notebooks/eulers_method.ipynb)* (Note: This module will be updated shortly after the publication of this notebook). \n",
"\n",
"From a programming perspective, the level of this notebook is quite basic, but being familiar with basic Python and to a lesser extent the NumPy library is expected of the reader. For more information on the latter, check out our *[beginner-friendly notebook on numpy](https://nbviewer.jupyter.org/urls/www.numfys.net/media/notebooks/introduction_to_numpy.ipynb)*.\n",
"\n",
"Lastly, we would like to explain the choice of what kind of physical system we are going to solve. The most crude models for modeling bacterial growth is an excellent choice for demonstrating Euler's method, as the differential equation governing this growth is quite simple."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Theory\n",
"\n",
"### Population growth\n",
"Before we start programming, we will give a short introduction to bacterial growth. Bacteria reproduce by binary fission [[1]](#rsc). This is a process where a single bacterial cell splits in two, creating two bacterial cells. The two new bacterial cells, can again split into two, thus creating four bacterial cells. In reality, a single bacterial cell can only split in two a certain amount of times, but in our project we model our growth rate as if this was not the case.\n",
"\n",
"We can then write our differential equation as\n",
"\n",
"\\begin{equation}\n",
"\\frac{dy}{dt} = ky(t),\n",
"\\label{ODE}\n",
"\\end{equation}\n",
"\n",
"where $y(t)$ is the population $y$ at time $t$, and $k$ is some constant of proportionality. If we use days as time unit, and assume that the population size at $ t= 1$ is double the population size at the $t=0$\n",
"\n",
"\\begin{equation}\n",
"y(1) = 2y(0)\n",
"\\label{Initial},\n",
"\\end{equation}\n",
"\n",
"we can solve the differential equation analytically. Combining equations \\eqref{ODE} and \\eqref{Initial}, we get\n",
"\n",
"\\begin{equation}\n",
"y(t) = \\mathrm{e}^{kt} = \\mathrm{e}^{\\mathrm{ln}(2)t} = 2^{t}. \n",
"\\label{Ana_sol}\n",
"\\end{equation}\n",
"\n",
"Equation \\eqref{Ana_sol} fully describes the population size at time $t$.\n",
"\n",
"### Euler's method\n",
"This paragraph will try to convey the bare minimum of theory regarding Euler's method. Again, we strongly recommend reading our full module on *[Euler's method](https://nbviewer.jupyter.org/urls/www.numfys.net/media/notebooks/eulers_method.ipynb)*, as some of the concepts might not be presented at adequate depth. However, these paragraphs should be sufficient for the implementation.\n",
"\n",
"First of all, when solving differential equations numerically, we need to __discretize__ our time variable $t$. $t$ is no longer a continuous variable, instead we write\n",
"\n",
"$$\n",
"t_n = t_0 + nh, \\quad \\mathrm{with} \\quad n = 0, 1, 2,..., N,\n",
"$$\n",
"\n",
"where $t_0$ is the time value where we know our initial population size, and $h$ is the size between adjacent discrete time values. The relation between $N$ and $h$ is given by\n",
"\n",
"$$\n",
"h = \\frac{t_N - t_0}{N},\n",
"$$\n",
"\n",
"where $N$ is the number of discrete time points we have in our simulation, while $t_N$ and denote the largest time value we have in our simulation.\n",
"\n",
"In general, our numerical approximation will be better if we choose a small $h$. Note as the size of $h$ decreases, the number of discrete time values between $t_0$ and $t_N$ increases. We pay for the increased level precision by increasing the number of calculations needed, thus increasing the runtime of our program.\n",
"\n",
"A first order differential equation with no explicit time dependence can be written on the the most general form\n",
"\n",
"\\begin{equation}\n",
"\\frac{dy}{dt} = g(y),\n",
"\\label{gen_Euler}\n",
"\\end{equation}\n",
"\n",
"where $g(y)$ is the equation governing the rate of change of our function $y(t)$. In our case, $g(y) = ky$.\n",
"\n",
"If we know the population size at $t_0$ and denote this value as $y_0$, we can use Euler's method to find an approximation of the population size at $t_1 = t_0 +h$. The population size at $t_1$ is denoted as $y_1$. This approximation can be calculated by the formula\n",
"\n",
"$$\n",
"y_1 = y_0 + hg(y_0).\n",
"$$\n",
"\n",
"Now, to find the population size $y_2$ at $t_2 = t_1 + h = t_0 + 2h$, we use the same formula, but with $y_1$ instead of $y_0$\n",
"\n",
"$$\n",
"y_2 = y_1 + h g(y_1).\n",
"$$\n",
"\n",
"The most general form of Euler's method is written as\n",
"\n",
"$$\n",
"y_{n+1} = y_n + h g(y_n),\n",
"\\label{Euler}\n",
"$$\n",
"where we have the initial condition that\n",
"\n",
"$$\n",
"y(t_0) = y_0.\n",
"$$\n",
"\n",
"Now we can implement Euler's method in Python, and compare our numerical results to the analytical solution given in equation \\eqref{Ana_sol}.\n",
"\n",
"## Implementation"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [],
"source": [
"# Importing the necessary libraries\n",
"import numpy as np # NumPy is used to generate arrays and tp perform some mathematical operations\n",
"import matplotlib.pyplot as plt # Used for plotting results\n",
"\n",
"# Updating figure params\n",
"# Note, this is not important for any of the code, this is just to set the appropiate figure and text sizes\n",
"newparams = {'figure.figsize': (15, 7), 'axes.grid': False,\n",
" 'lines.markersize': 10, 'lines.linewidth': 2,\n",
" 'font.size': 15, 'mathtext.fontset': 'stix',\n",
" 'font.family': 'STIXGeneral', 'figure.dpi': 200}\n",
"plt.rcParams.update(newparams)"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [],
"source": [
"def step_Euler(y, h, f):\n",
" \"\"\"This Python function performs a single step of Euler's method.\n",
" \n",
" Parameters:\n",
" y: Numerical approximation of y at time t\n",
" h: Step size\n",
" f: RHS of our ODE (RHS = Right hand side). Can be any function that only has y as a variable.\n",
" Returns:\n",
" next_y: Numerical approximation of y at time t+h\n",
" \"\"\"\n",
" next_y = y + h * f(y)\n",
" return next_y\n",
"\n",
"\n",
"def full_Euler(h, f, y_0 = 1, start_t = 0, end_t = 1):\n",
" \"\"\" A full numerical aproximation of an ODE in a set time interval. Performs consecutive Euler steps\n",
" with step size h from start time until the end time. Also takes into account the initial values of the ODE\n",
" \n",
" Parameters:\n",
" h: Step size\n",
" f: RHS of our ODE\n",
" y_0 : Initial condition for y at t = start_t\n",
" start_t : The time at the initial condtion, t_0\n",
" end_t : The end of the interval where the Euler method is perfomed, t_N\n",
" Returns:\n",
" y_list: Numerical approximation of y at times t_list\n",
" t_list: Evenly spaced discrete list of time with spacing h. \n",
" Starting time = start_t, and end time = end_t \n",
" \"\"\"\n",
" # Number of discretisation steps\n",
" N = int((end_t - start_t) / h)\n",
" # Following the notation in the theory, we have N+1 discrete time values linearly spaced\n",
" t_list = np.linspace(start_t, end_t, N + 1)\n",
" \n",
" # Initialise array to store y-values\n",
" y_list = np.zeros(N + 1)\n",
" # Assign initial condition to first element\n",
" y_list[0] = y_0\n",
" \n",
" # Assign the rest of the array using N Euler_steps\n",
" for i in range(0, N):\n",
" y_list[i + 1] = step_Euler(y_list[i], h, f)\n",
" # With N + 1 time values, we are only able to calculate N values of y. Thus we do not return the last element of\n",
" # our time list. We accomplish this by writing t_list[:-1]\n",
" return y_list, t_list "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now that we have our functions defined, we can simulate the bacterial population. We only need to define our RHS (Right hand side) of our differential equation, which we in the theory part denoted as $g(y)$."
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [
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