{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "In this notebook, we'll be working on a classic problem: solving the harmonic oscillator equation. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Introduction: the harmonic oscillator" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "What's an [harmonic oscillator](https://en.wikipedia.org/wiki/Harmonic_oscillator)? It's a relatively simple model for natural systems that finds wide applications. \n", "\n", "A classical example of such a system is a mass that is connected to a spring. If the mass $m$ is located according to the coordinates $x(t)$, and the spring stiffness is $k$, then Newton's equations of momentum read:\n", "\n", "$$\n", "m \\ddot{x} + k x = 0\n", "$$\n", "\n", "Let's simplify the notation in the following way:\n", "\n", "$$\n", "\\ddot{x} + \\omega_0^2 x = 0\n", "$$\n", "\n", "where $\\omega_0^2 = \\frac{k}{m}$. The above equation is the harmonic oscillator model equation. This equation alone does not allow numerical computing unless we also specify initial conditions, which define the oscillator's state at the time origin.\n", "\n", "Since we have a second derivative in time of the position $x$, we need to specify two things: the initial position and the initial speed (i.e. time derivative) of the oscillator. These are denoted as: \n", "\n", "$$\n", "\\begin{align}\n", "x(t = 0) = x_0 \\\\\n", "\\dot{x}(t=0) = \\dot{x}_0\n", "\\end{align}\n", "$$\n", "\n", "In this notebook, we will explore three options for solving the evolution problem of this harmonic oscillator:\n", "\n", "- solve it analytically using `sympy`\n", "- solve it numerically by implementing a finite difference scheme from scratch\n", "- solve it numerically with `scipy` builtin tools" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Analytical solution with sympy" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To solve this equation analytically, we will use sympy. Sympy provides an ordinary differential equation (ODE) module for these problems: ." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First, we define our symbols and function:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import sympy\n", "\n", "sympy.init_printing()\n", "\n", "m, k, x_0, xdot_0, omega_0, t = sympy.symbols('m, k, x_0, xdot_0, omega_0, t')\n", "x = sympy.Function('x')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can then use `dsolve`, which deals with differential equations:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$\\displaystyle x{\\left(t \\right)} = C_{1} e^{- i \\omega_{0} t} + C_{2} e^{i \\omega_{0} t}$" ], "text/plain": [ " -ⅈ⋅ω₀⋅t ⅈ⋅ω₀⋅t\n", "x(t) = C₁⋅ℯ + C₂⋅ℯ " ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sol = sympy.dsolve(sympy.Derivative(x(t), t, 2) + omega_0**2 * x(t))\n", "sol" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And define our initial conditions and solve for them:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$\\displaystyle \\left[ C_{1} + C_{2} = x_{0}, \\ - i C_{1} \\omega_{0} + i C_{2} \\omega_{0} = \\dot{x}_{0}\\right]$" ], "text/plain": [ "[C₁ + C₂ = x₀, -ⅈ⋅C₁⋅ω₀ + ⅈ⋅C₂⋅ω₀ = ẋ₀]" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ics = [sympy.Eq(sol.args[1].subs(t, 0), x_0), sympy.Eq(sol.args[1].diff(t).subs(t, 0), xdot_0)]\n", "ics" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$\\displaystyle \\left[ \\left\\{ C_{1} : \\frac{\\omega_{0} x_{0} + i \\dot{x}_{0}}{2 \\omega_{0}}, \\ C_{2} : \\frac{\\omega_{0} x_{0} - i \\dot{x}_{0}}{2 \\omega_{0}}\\right\\}\\right]$" ], "text/plain": [ "⎡⎧ ω₀⋅x₀ + ⅈ⋅ẋ₀ ω₀⋅x₀ - ⅈ⋅ẋ₀⎫⎤\n", "⎢⎨C₁: ────────────, C₂: ────────────⎬⎥\n", "⎣⎩ 2⋅ω₀ 2⋅ω₀ ⎭⎦" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "solved_ics = sympy.solve(ics)\n", "solved_ics" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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OPpTZCzm2+IJiQkkBpKXAM2UMjAJVUUCyy+LKxkJVXGkaU1SVMWSj5jAwGaBuTz5rAwoKwErCCvpRjrinGtS8JIwFdiUHvNHzkM/6oKSCEnMF7ccoUAkFbCxUwoi0GaaoUmqcaFjKhY/QdoLyYCXFbb6QWfFckEivsIck/GBZoZhCmHiUVOkSBmkGRoHNKGBjYTPSd1ZsZ1Sd5LHEKRTQoEcZoaBQTDkESy2Pt2ejwNFRwMbCNJaaoppGPyvdTwG2AjnPcqABS/iTH7g+1jyjwElQwMbCgWy2b/0dSDgrNpwCUkrpC79cc08vXAxHZDmNAnecAjYWDmPg/wF3W4utSSA4HgAAAABJRU5ErkJggg==\n", "text/latex": [ "$\\displaystyle x{\\left(t \\right)} = \\frac{\\left(\\omega_{0} x_{0} - i \\dot{x}_{0}\\right) e^{i \\omega_{0} t}}{2 \\omega_{0}} + \\frac{\\left(\\omega_{0} x_{0} + i \\dot{x}_{0}\\right) e^{- i \\omega_{0} t}}{2 \\omega_{0}}$" ], "text/plain": [ " ⅈ⋅ω₀⋅t -ⅈ⋅ω₀⋅t\n", " (ω₀⋅x₀ - ⅈ⋅ẋ₀)⋅ℯ (ω₀⋅x₀ + ⅈ⋅ẋ₀)⋅ℯ \n", "x(t) = ────────────────────── + ───────────────────────\n", " 2⋅ω₀ 2⋅ω₀ " ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "full_sol = sol.subs(solved_ics[0])\n", "full_sol" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The above equation was obtained by sympy and contains the solution to our problem. We can notice that it features complex exponentials, hinting at the oscillatory functions we already expect from our physical knowledge of harmonic oscillator.\n", "\n", "Let's plot the solution for two different initial condition sets: \n", "\n", "- case 1 : initial position is non-zero and initial velocity is zero \n", "- case 2 : initial position is zero and initial velocity is non-zero\n", "\n", "We'll use a value of $\\omega_0$ equal to 2 (it's often helpful to not choose a value of 1 for constants to spot mistakes early)." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$\\displaystyle x{\\left(t \\right)} = \\cos{\\left(2 t \\right)}$" ], "text/plain": [ "x(t) = cos(2⋅t)" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "case1 = sympy.simplify(full_sol.subs({x_0:1, xdot_0:0, omega_0:2}))\n", "case1" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "text/plain": [ "" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sympy.plot(case1.rhs)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's look at our second solution." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$\\displaystyle x{\\left(t \\right)} = \\frac{\\sin{\\left(2 t \\right)}}{2}$" ], "text/plain": [ " sin(2⋅t)\n", "x(t) = ────────\n", " 2 " ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "case2 = sympy.simplify(full_sol.subs({x_0:0, xdot_0:1, omega_0:2}))\n", "case2" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "text/plain": [ "" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sympy.plot(case2.rhs)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Okay, now on to numerical solving with our own solution." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Numerical solution using finite differences" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's discretize our problem as an explicite [finite difference scheme](https://en.wikipedia.org/wiki/Finite_difference_method). The problem becomes:\n", "\n", "$$\n", "\\left\\{\n", "\\begin{align}\n", "x^{n+1} = && (2 - \\omega_0^2dt^2)x^n - x^{n-1} \\\\\n", "x^0 = && x_0 \\\\\n", "x^1 = && x_0 + \\dot{x}_0 dt\n", "\\end{align}\n", "\\right.\n", "$$\n", "\n", "As we can see from the equation above, we need to keep track of the two previous positions $x^n$ and $x^{n-1}$ to compute the solution for the next time step. Also, the value $x^1$ is computed from the knowledge of the initial speed by a first order Taylor approximation.\n", "\n", "\n", "To solve this, I wrote a class in the next cell called `HarmonicOdeSolver`. It provides two methods, apart from `__init__`:\n", "\n", "- `step` that iterates the numerical system one single step in time\n", "- `step_until` that iterates the numerical system until a given time and returns snapshots of the solution at certain points chosen by the user\n" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "plt.style.use('bmh')\n", "\n", "class HarmonicOdeSolver:\n", " def __init__(self, dt, x0, xd0, omega_squared):\n", " \"Inits the solver.\"\n", " self.dt = dt\n", " self.dt_squared = dt**2\n", " self.t = dt\n", " self.omega_squared = omega_squared\n", " self.x0 = x0\n", " self.xd0 = xd0\n", " self.x = [xd0 * dt + x0, x0]\n", " \n", " def step(self):\n", " \"Steps the solver.\"\n", " xt, xtm1 = self.x\n", " xtp1 = (2 - self.omega_squared * self.dt_squared) * xt - xtm1\n", " self.x = (xtp1, xt)\n", " self.t += self.dt\n", " \n", " def step_until(self, tmax, snapshot_dt):\n", " \"Steps the solver until a given time, returns snapshots.\"\n", " ts = [self.t]\n", " vals = [self.x[0]]\n", " niter = max(1, int(snapshot_dt // self.dt))\n", " while self.t < tmax:\n", " for _ in range(niter):\n", " self.step()\n", " vals.append(self.x[0])\n", " ts.append(self.t)\n", " return np.array(ts), np.array(vals)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's test this implementation." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "snapshot_dt = 0.15\n", "\n", "solver = HarmonicOdeSolver(2e-1, 1, 0, 4)\n", "\n", "ts, vals = solver.step_until(12, snapshot_dt)\n", "\n", "plt.plot(ts, vals);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's compare this to sympy." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(ts, vals, 'x', label='my own ode solver')\n", "plt.plot(ts, sympy.lambdify(t, case1.rhs, 'numpy')(ts), label='sympy')\n", "plt.legend(loc='upper right');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Okay, that's pretty good, except the ode solver lags a bit behind the sympy solution (this is due to the computation of $x^1$ that is a pretty bad approximation). Let's try again with a smaller `dt`." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "solver = HarmonicOdeSolver(1e-3, 1, 0, 4)\n", "\n", "ts, vals = solver.step_until(12, snapshot_dt)\n", "\n", "plt.plot(ts, vals, 'x', label='my own ode solver')\n", "plt.plot(ts, sympy.lambdify(t, case1.rhs, 'numpy')(ts), label='sympy')\n", "plt.legend(loc='upper right');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Okay, looks good. What about the second case?" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "solver = HarmonicOdeSolver(1e-3, 0, 1, 4)\n", "ts, vals = solver.step_until(12, snapshot_dt)\n", "\n", "plt.plot(ts, vals, 'x', label='my own ode solver')\n", "plt.plot(ts, np.real(sympy.lambdify(t, case2.rhs, 'numpy')(ts)), label='sympy')\n", "plt.legend(loc='upper right');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Okay, good again!\n", "Let's move on to the last part of this exploration." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Numerical solution using Scipy " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Scipy offers a number of tools for dealing with ordinary differential equations: . \n", "Here, we'll use the [`odeint`](https://docs.scipy.org/doc/scipy-0.18.1/reference/generated/scipy.integrate.odeint.html#scipy.integrate.odeint) routine.\n", "\n", "The documentation says that this routine solves first order differential equations. This means that we need to recast our problem as a first order system. To do this, we write out a vector of unknowns:\n", "\n", "$$\n", "u = \n", "\\begin{pmatrix}\n", "\\dot{x} \\\\\n", "x\n", "\\end{pmatrix}\n", "$$\n", "\n", "Hence we can write:\n", "\n", "$$\n", "\\frac{d}{dt}\n", "\\begin{pmatrix}\n", "\\dot{x} \\\\ x\n", "\\end{pmatrix} =\n", "\\begin{pmatrix}\n", "-\\omega_0^2 x \\\\ \\dot{x}\n", "\\end{pmatrix}\n", "$$\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can now write out the derivative, or the right hand side of the previous equation assuming we give our vector $u$ as input:" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "def deriv(u, t, omega_squared):\n", " \"Provides derivative of vector u.\"\n", " xdot, x = u\n", " return [-omega_squared * x, xdot]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's solve case 1 using this. We define a time vector." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "ts = np.arange(0, 12, snapshot_dt)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And initial conditions." ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "y0 = [0, 1]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we integrate and look at the result." ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from scipy.integrate import odeint\n", "scipysol = odeint(deriv, y0, ts, args=(4,))\n", "\n", "plt.plot(ts, scipysol[:, 1]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's compare it again with our reference solution:" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(ts, scipysol[:, 1], 'x', label='scipy')\n", "plt.plot(ts, sympy.lambdify(t, case1.rhs, 'numpy')(ts), label='sympy')\n", "plt.legend(loc='upper right');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This works nicely. What about the second test case?" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "y0 = [1, 0]\n", "\n", "scipysol = odeint(deriv, y0, ts, args=(4,))\n", "\n", "plt.plot(ts, scipysol[:, 1], 'x', label='scipy')\n", "plt.plot(ts, np.real(sympy.lambdify(t, case2.rhs, 'numpy')(ts)), label='sympy')\n", "plt.legend(loc='upper right');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Conclusions " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this article, we've solved an ordinary differential equation in three different ways. First, we solved it exactly using an analytical approach (for which sympy did all the heavy lifting). Then, we implemented our own finite difference scheme. Finally, we used one of the builtin solvers of scipy to solve the equation. What we can say is:\n", "\n", "- analytical solutions, when available, are the most useful\n", "- implementing our own scheme is doable, but is a lot of work if we're not specialists in numerical computation and likely more complex in cases that are not like this one-dimensional oscillator\n", "- using scipy is definitely recommended since all the complicated things from the finite differences are done for us (this strategy could be described as [\"standing on the shoulders of giants\"](https://en.wikipedia.org/wiki/Standing_on_the_shoulders_of_giants)) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*This post was entirely written using the Jupyter Notebook. Its content is BSD-licensed. You can see a static view or download this notebook with the help of nbviewer at [20170414_HarmonicOscillator.ipynb](http://nbviewer.ipython.org/urls/raw.github.com/flothesof/posts/master/20170414_HarmonicOscillator.ipynb).*" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.3" } }, "nbformat": 4, "nbformat_minor": 1 }