{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text",
"id": "view-in-github"
},
"source": [
"![\"Open](\"https://colab.research.google.com/assets/colab-badge.svg\")
"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "FcrvMePu9oqE"
},
"source": [
"# Implicit methods"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "10pBqPn49zPX"
},
"source": [
"Up until this point, we have been discussing *explicit* solver schemes, in which $y_{i+1}$ is determined using the information $x_i$ and $y_i$ with kowledge of $f(x_i, y_i)$. \n",
"\n",
"*Implicit* methods uses information at the new time step, in order to determine it; i.e.: using $f(x_{i+1}, y_{i+1})$! The new value of $y_{i+1}$ is therefore calcualted implicitly, for which we will generally need to use a root finder. The root finder adds significant computational expense but is substantially less sensative to numerical instability."
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "tHu90oYFr-EB"
},
"source": [
"### The Backward Euler method"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "v9rvlLCAwfrf"
},
"source": [
"The simplest implicit scheme is the implicit Euler method (backward Euler). Like the forward Euler method we assumes a constant slope over the timestep but this time it is the slope *at the end of the timestep*:\n",
"\n",
"$$ y_{i+1} = y_i + f(x_{i+1}, y_{i+1}) h$$\n",
"\n",
"which implicitly defines $y_{i+1}$."
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "UguKGVmnmElD"
},
"source": [
"## Numerical instability"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "VGqayrdRmLdm"
},
"source": [
"An algorithm is numerically unstable when small errors that occur during computation grow. Such errors can occur due to user-choices (e.g. - too large a step size) or simply round-off/truncation error.\n",
"\n",
"NB: numerical instability is a property of the *algorithm*, not the equation."
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "2QK2V--Ly6Ir"
},
"source": [
"#### Example: Initial value problem"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "j6cg_XFey_3S"
},
"source": [
"Integrate $$\\frac{\\partial y}{\\partial t} = - y$$\n",
"\n",
"from 0 to 20 using the forward and backward Euler methods and compare to the exact solution,\n",
"$$ y(t) = e^{-t}$$\n",
"\n",
"for varying step sizes."
]
},
{
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"execution_count": 14,
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"interactive(children=(FloatSlider(value=0.8, description='h', max=5.0, min=0.1), Output()), _dom_classes=('wid…"
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"source": [
"# prompt: Can you make the above plot a slider for the step size ontop of the plot\n",
"\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from ipywidgets import interact, FloatSlider\n",
"\n",
"\n",
"def plot_with_slider(h):\n",
" t0 =0\n",
" t_end = 20\n",
" y0 = 2\n",
" # Time points\n",
" t_points = np.arange(t0, t_end + h, h)\n",
"\n",
" # Analytical solution\n",
" y_analytical = y0 * np.exp(-t_points)\n",
"\n",
" # Explicit Euler method\n",
" y_explicit = np.zeros_like(t_points)\n",
" y_explicit[0] = y0\n",
" for i in range(1, len(t_points)):\n",
" y_explicit[i] = y_explicit[i-1] * (1 - h)\n",
"\n",
" # Implicit Euler method\n",
" y_implicit = np.zeros_like(t_points)\n",
" y_implicit[0] = y0\n",
" for i in range(1, len(t_points)):\n",
" y_implicit[i] = y_implicit[i-1] / (1 + h)\n",
"\n",
" # Plotting the results\n",
" plt.figure(figsize=(10, 6))\n",
" plt.plot(t_points, y_analytical, label='Analytical Solution', color='black', linestyle='--')\n",
" plt.plot(t_points, y_explicit, label='Explicit Euler', color='blue', marker='o')\n",
" plt.plot(t_points, y_implicit, label='Implicit Euler', color='red', marker='x')\n",
" plt.xlabel('Time')\n",
" plt.ylabel('y(t)')\n",
" plt.xlim(0, 20)\n",
" plt.title('Comparison of Explicit and Implicit Euler Methods')\n",
" plt.legend()\n",
" plt.grid(True)\n",
" plt.show()\n",
"\n",
"interact(plot_with_slider, h=FloatSlider(min=.1, max=5, step=.1, value=0.8));"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "FlJ_MGgv9F-5"
},
"source": [
"Gadzooks!\n",
"\n",
"Let's consider the Forward Euler scheme analytically. For generality, say $\\frac{dy}{dt} = -ay$ for some positive constant $a$,\n",
"\n",
"$$\\begin{align}\n",
"y_{i+1} &= y_i+h \\frac{dy}{dt}(y_{i}) \\\\\n",
"&= y_i - y_i a h \\\\\n",
"&= y_i [1-a h]\n",
"\\end{align} $$\n",
"\n",
"In order for the solution to follow the smoothly decreasing behaviour, $h\\lt\\frac{1}{a}$. If $\\frac{1}{a}\\lt h \\lt \\frac{2}{a}$, the solution will overshoot but eventually correct itself. But if $h \\gt \\frac{2}{a}$ the method will catasrophically overcorrect!"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "LPg8SbGb-lkn"
},
"source": [
"Compare this to the implicit case,\n",
"\n",
"$$\\begin{align}\n",
"y_{i+1} &= y_i+h \\frac{dy}{dt}(y_{i+1}) \\\\\n",
"&= y_i - y_{i+1} a h \\\\\n",
"y_{i+1}&= \\frac{y_i}{1+ah}\n",
"\\end{align} $$\n",
"\n",
"which is nicely decreasing for all $h>0$ and is therefore *unconditionally stable*!\n",
"\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "X9tjQzbl_cUl"
},
"source": [
"Numerical stability has therefore placed a limit on the step size for which a method will converge on the correct answer. There are different types of stability, which is outside the scope of this course.\n",
"\n",
"The stability of the explicit vs implicit Euler methods helps show some intuition on what's going on: since implicit schemes focus on the end of the time step and how we *got there*, they are less sensative to errors introduced by large time steps or numerical noise."
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "ki7fDZoWYhsq"
},
"source": [
"##Stiffness"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "KPyTWu6GYusZ"
},
"source": [
"One might think that the adaptive time steppers may dynamically avoid numerical instability but you would be dissappointed...\n",
"\n",
"Consider the equation\n",
"$$ \\frac{dy}{dt} = -1000 y + 3000 - 2000 e^{-t}$$ with $y(0) = 0$.\n",
"\n",
"The analytical solution is $$y(t) = 3-0.998 e^{-1000 t} - 2.0-2 e^{-t}$$ which features a fasts transient due to $e^{-1000 t}$ followed by a slow progression:"
]
},
{
"cell_type": "code",
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"ea677e31f8294205981f03a25d5a15f5",
"2b1f205f829f4b478de8143bdeccb714",
"4ce49556ee414aeaaad5c53de9ce20d4",
"5f67a598594c42afb680e40afeaeaed4"
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"interactive(children=(FloatSlider(value=3.0, description='limit', max=5.0, min=0.1), Output()), _dom_classes=(…"
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],
"source": [
"# prompt: plot 3-0.998 e^{-1000 t} - 2.0-2 e^{-t} from 0 to a limit determined by a slider starting at 3\n",
"\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from ipywidgets import interact, FloatSlider\n",
"\n",
"def plot_function(limit):\n",
" t = np.linspace(0, limit, 500)\n",
" y = 3 - 0.998 * np.exp(-1000 * t) - 2 - 2 * np.exp(-t)\n",
" plt.figure(figsize=(10, 6))\n",
" plt.plot(t, y)\n",
" plt.xlabel('t')\n",
" plt.ylabel('y(t)')\n",
" plt.title('Plot of y(t) = 3 - 0.998e^(-1000t) - 2 - 2e^(-t)')\n",
" plt.grid(True)\n",
" plt.show()\n",
"\n",
"interact(plot_function, limit=FloatSlider(min=.1, max=5, step=0.1, value=3));"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "IHf0foZVbOd1"
},
"source": [
"The stability of the fast term with forward Euler requires $h\\lt \\frac{2}{1000}$ to not catastrophically overcorrect, but at least that is only for the first little bit right?\n",
"\n",
"Wrong. Even though the transient only dominates the behaviour for the first little bit, it is still there for the rest, and will still tear shirt up!"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
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"interactive(children=(FloatSlider(value=0.0005, description='h', max=0.003, min=0.0001, readout_format='.4f', …"
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],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from ipywidgets import interact, FloatSlider\n",
"\n",
"\n",
"def plot_with_slider(h):\n",
" t0 =0.01\n",
" t_end = .05\n",
" y0 = 0.\n",
" # Time points\n",
" t_points = np.arange(t0, t_end + h, h)\n",
"\n",
" # Analytical solution\n",
" def y_true(t):\n",
" return 3. - 0.998*np.exp(-1000*t) - 2.002*np.exp(-t)\n",
" y_analytical = y_true(t_points)\n",
"\n",
" y0 = y_true(t0)\n",
"\n",
" def f(y,t):\n",
" return -1000.*y + 3000. - 2000.*np.exp(-t)\n",
"\n",
" # Explicit Euler method\n",
" y_explicit = np.zeros_like(t_points)\n",
" y_explicit[0] = y0\n",
" for i in range(1, len(t_points)):\n",
" y_explicit[i] = y_explicit[i-1] + f(y_explicit[i-1], t_points[i-1]) * h\n",
"\n",
" # Implicit Euler method\n",
" y_implicit = np.zeros_like(t_points)\n",
" y_implicit[0] = y0\n",
" def imp(y, t, y0, f, h):\n",
" return y - (y0 + h*f(y, t))\n",
"\n",
" from scipy.optimize import root\n",
" for i in range(1, len(t_points)):\n",
" sol = root(imp, y_implicit[i-1], args=(t_points[i], y_implicit[i-1], f, h))\n",
" y_implicit[i] = sol.x[0]\n",
"\n",
" # Plotting the results\n",
" plt.figure(figsize=(10, 6))\n",
" plt.plot(t_points, y_analytical, label='Analytical Solution', color='black', linestyle='--')\n",
" plt.plot(t_points, y_explicit, label='Explicit Euler', color='blue', marker='o')\n",
" plt.plot(t_points, y_implicit, label='Implicit Euler', color='red', marker='x')\n",
" plt.xlabel('Time')\n",
" plt.ylabel('y(t)')\n",
" plt.xlim(t0, t_end)\n",
" plt.title('Comparison of Explicit and Implicit Euler Methods')\n",
" plt.legend()\n",
" plt.grid(True)\n",
" plt.show()\n",
"\n",
"interact(plot_with_slider, h=FloatSlider(min=.0001, max=.003, step=.0001, value=0.0005, readout_format='.4f'));"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "N0e705kpWlZF"
},
"source": [
"###Definition of stiffness"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "my2n72JvXlMi"
},
"source": [
"A precise mathematical definition of stiffness is difficult, but in general: A stiff equation is one in which accuracy of the solution is determined by numerical stability rather than the behaviour of the solution.\n",
"\n",
"This is expecially problematic in physics where short transients as a system reaches a 'well behaved state' are common. If we include the phenomena which describe the transients, we are bound by their timescales weather or not the transient has died off!\n",
"\n",
"One approach is to ignore the transients entirely! Examples include:\n",
"- Quasistatic elasticity\n",
"- diffusive heat / mass transport\n",
"- etc.\n",
"\n",
"Alternately, we can use implicit methods which are more stable, but come with added computational expense."
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "qJby4GEIWKKT"
},
"source": [
"## Implicit Runge-Kutta methods"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "_IDpM3_PYxkd"
},
"source": [
"We are now in a position to generalize the RK methods. Recalling:\n",
"\n",
"$$ y_{i+1} \\approx y_i + h \\sum_{n=1}^s a_n k_n$$\n",
"\n",
"with\n",
"\n",
"$$\n",
"k_n = f(x_i + p_n, y_i + \\sum_{m=1}^s q_{nm}k_m)\n",
"$$\n",
"\n",
"the Butcher tableau now expanded:\n",
"\n",
"\n",
"$$\n",
"\\begin{array}{c|cccc}\n",
"p_1 & q_{11} & q_{12} & \\dots & q_{1s} \\\\\n",
"p_2 & q_{21} & q_{22} & \\dots & q_{2s} \\\\\n",
"\\vdots & \\vdots & \\vdots & \\ddots & \\vdots \\\\\n",
"p_s & q_{s1} & q_{s2} & \\dots & q_{ss} \\\\\n",
"\\hline\n",
" & a_1 & a_2 & \\dots & a_s\n",
"\\end{array}\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "3TSuy_9WqloY"
},
"source": [
"In explicit methods, the $k_n$s could be built progressively on $k_{n-1...}$, but this is not the case for implicit RK. Rather, a set of $k_n$ may need to be solved *simultaneously* which can dramatically amplify the computaitonal expense.\n",
"\n",
"The balance of computaional expense to increased accuracy has motivated a plethora of RK methods of varying stages, orders, and complexity of which we will only discuss a few:"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "cpye2ouIZ3YJ"
},
"source": [
"### Implicit Euler method"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "aJ8ebS6PbJpi"
},
"source": [
"The Implicit Euler, $$ y_{i+1} = y_i + f(x_{i+1}, y_{i+1}) h$$ has the tableau:"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "kdw7YDDNa7Eh"
},
"source": [
"$$\n",
"\\begin{array}{c|c}\n",
"1 & 1 \\\\\n",
"\\hline\n",
" & 1 \\\\\n",
"\\end{array}\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "_l1wcs30b6bW"
},
"source": [
"### RK2 implicit"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "eg_44h8wb-vG"
},
"source": [
"#### Implicit midpoint method\n",
"\n",
"$$ \\begin{align}\n",
"y_{i+1} &= y_i + h k_1\n",
"\\end{align}$$\n",
"where\n",
"\n",
"$$k_1 = f(x_{i+\\frac{1}{2}}, y_{i+\\frac{1}{2}}) $$\n",
"which is found through the implicit solution of:\n",
"$$y_{i+\\frac{1}{2}} = y_n + \\frac{h}{2} f\\big(x_i+\\frac{1}{2}h, y_{i+\\frac{1}{2}}\\big)$$\n",
"\n",
"\n",
"\n",
"\n",
"and has the Butcher Tableau,\n",
"$$\n",
"\\begin{array}{c|c}\n",
"\\frac{1}{2} & \\frac{1}{2} \\\\\n",
"\\hline\n",
" & 1 \\\\\n",
"\\end{array}\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "R1osRIWfcViQ"
},
"source": [
"#### Implicit trapezoid / Crank-Nicholson method\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "a3kMMWh1ckk5"
},
"source": [
"$$\n",
"y_{n+1} = y_n + \\frac{h}{2} \\left( f(t_n, y_n) + f(t_{n+1}, y_{n+1}) \\right)\n",
"$$\n",
"\n",
"with Tableau\n",
"$$\n",
"\\begin{array}{c|cc}\n",
"0 & 0 & 0 \\\\\n",
"1 & \\frac{1}{2} & \\frac{1}{2} \\\\\n",
"\\hline\n",
" & \\frac{1}{2} & \\frac{1}{2} \\\\\n",
"\\end{array}\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "5FC5x1lrc_pr"
},
"source": [
"#### Gauss-Legendre order 4 (2 stages)"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "TSIAJWZIdESO"
},
"source": [
"As an example of the complexity, the Gauss-Legendre order 4 method has a tableau,\n",
"$$\n",
"\\begin{array}{c|cc}\n",
"\\frac{1}{2} - \\frac{\\sqrt{3}}{6} & \\frac{1}{4} & \\frac{1}{4} - \\frac{\\sqrt{3}}{6} \\\\\n",
"\\frac{1}{2} + \\frac{\\sqrt{3}}{6} & \\frac{1}{4} + \\frac{\\sqrt{3}}{6} & \\frac{1}{4} \\\\\n",
"\\hline\n",
" & \\frac{1}{2} & \\frac{1}{2} \\\\\n",
"\\end{array}\n",
"$$\n",
"\n",
"such that\n",
"\n",
"$$\n",
"\\begin{align*}\n",
"k_1 &= f\\left(t_n + \\left(\\frac{1}{2} - \\frac{\\sqrt{3}}{6}\\right)h, y_n + h\\left(\\frac{1}{4}k_1 + \\left(\\frac{1}{4} - \\frac{\\sqrt{3}}{6}\\right)k_2\\right)\\right) \\\\\n",
"k_2 &= f\\left(t_n + \\left(\\frac{1}{2} + \\frac{\\sqrt{3}}{6}\\right)h, y_n + h\\left(\\left(\\frac{1}{4} + \\frac{\\sqrt{3}}{6}\\right)k_1 + \\frac{1}{4}k_2\\right)\\right)\n",
"\\end{align*}\n",
"$$\n",
"\n",
"with the update for \\( y_{n+1} \\) is then given by:\n",
"\n",
"$$\n",
"y_{n+1} = y_n + h\\left(\\frac{1}{2}k_1 + \\frac{1}{2}k_2\\right)\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "9Ng0UeNddYo8"
},
"source": [
"[and so on](https://en.wikipedia.org/wiki/List_of_Runge%E2%80%93Kutta_methods)."
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "Ml6fo39pisTy"
},
"source": [
"## Systems of equations"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "GceD2pB0lnJ7"
},
"source": [
"In many engineering problems we will have a system of equations which depend on a single parameter:\n",
"\n",
"$$\\begin{align}\n",
"\\frac{dy_1}{dt} &= f_1(x, y_1, y_2, ..., y_j) \\\\\n",
"\\frac{dy_2}{dt} &= f_2(x, y_1, y_2, ..., y_j) \\\\\n",
"\\vdots \\\\\n",
"\\frac{dy_j}{dt} &= f_j(x, y_1, y_2, ..., y_j) \\\\\n",
"\\end{align}$$\n",
"\n",
"Happily, extension of the Runge-Kutta methods is straightforward! Collecting functions as a vector, we get the vector RK form:\n",
"\n",
"$$ \\vec{y}_{i+1} \\approx \\vec{y}_i + h \\sum_{n=1}^s a_n \\vec{k}_n$$\n",
"\n",
"with\n",
"\n",
"$$\n",
"\\vec{k}_n = \\vec{f}(x_i + p_n, \\vec{y}_i + \\sum_{m=1}^s q_{nm}\\vec{k}_m)\n",
"$$\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "RCHUwHMuiujX"
},
"source": [
"## Reduction of order"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "iqvc2GobqiJe"
},
"source": [
"Up to this point, we have only discussed first-order differential equations. Higher order differential equations can be reduced to a system of first order equations by defining new unknowns:\n",
"\n",
"$$ \\begin{align}\n",
"y^{\\prime\\prime} &= f(x, y, y^\\prime)\n",
"\\end{align} $$\n",
"\n",
"Let $z = y^\\prime$, such that\n",
"\n",
"$$ \\begin{align}\n",
"z^{\\prime} &= f(x, y, z) \\\\\n",
"y^{\\prime} &= z\n",
"\\end{align} $$\n",
"\n",
"which is solved as a system of equations as above.\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "zFivjfF_tspD"
},
"source": [
"#### Example: Swinging pendulum"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "MT43GmcQtzid"
},
"source": [
"The equation of motion of a swinging pendulum is,\n",
"$$ ml \\frac{d^2\\Theta(t)}{dt^2} = -m g \\sin\\big( \\Theta(t) \\big)$$"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "83spgYzntxIZ"
},
"source": [
""
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "EPw3L2njuUqS"
},
"source": [
"Use the reduction of order to write:\n",
"\n",
"$$ \\vec{y} = \\begin{bmatrix} \\Theta(t) \\\\ \\dot{\\Theta}(t) \\end{bmatrix} $$\n",
"\n",
"$$\\frac{d\\vec{y}}{dt} = \\begin{bmatrix} \\dot{\\Theta}(t) \\\\ \\ddot{\\Theta}(t) \\end{bmatrix} = \\begin{bmatrix} y_2 \\\\ g \\sin(y_1)/l \\end{bmatrix} = \\vec{f}(t, \\vec{y})$$"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 472
},
"id": "DDJ62rYxwEAm",
"outputId": "a827cc8f-b3ba-4bd9-e7d9-f23aebbf506a"
},
"outputs": [
{
"data": {
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"text/plain": [
""
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"source": [
"# prompt: Sovle the above with RK45\n",
"\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from scipy.optimize import root\n",
"from scipy.integrate import solve_ivp\n",
"\n",
"# Define the system of differential equations\n",
"def f(t, y):\n",
" theta, theta_dot = y\n",
" g = 9.81 # Acceleration due to gravity (m/s^2)\n",
" l = 1.0 # Length of the pendulum (m)\n",
" dydt = [theta_dot, (g/l) * np.sin(theta)]\n",
" return np.array(dydt)\n",
"\n",
"# Initial conditions\n",
"theta0 = np.pi/4 # Initial angle (radians)\n",
"theta_dot0 = 0.0 # Initial angular velocity (rad/s)\n",
"\n",
"# Time span\n",
"t_span = (0, 10)\n",
"\n",
"# Solve using RK45\n",
"sol = solve_ivp(f, t_span, [theta0, theta_dot0], method='RK45')\n",
"\n",
"# Plot the results\n",
"plt.plot(sol.t, sol.y[0, :])\n",
"plt.xlabel('Time (s)')\n",
"plt.ylabel('Theta (rad)')\n",
"plt.title('Pendulum Motion')\n",
"plt.grid(True)\n",
"plt.show()"
]
},
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"cell_type": "markdown",
"metadata": {
"id": "yqdwuL3GxEEL"
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"source": [
"#Multistep methods"
]
},
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"source": [
"Multistep methods are an approach to exploit the history of solutions $y_{\\le i}$ in the calculation of the next step $y_{i+1}$. Note that since they exploit a history, they require *bootstrapping* in order to get started.\n",
"\n",
"In general we know that\n",
"$$ \\begin{align}\n",
"\\frac{dy}{dx} &= f(x,y) \\\\\n",
"\\int dy &= \\int f(x,y) dx\\\\\n",
"y_{i+1} &= y_i + \\int f(x,y) dx\n",
"\\end{align}$$\n",
"\n",
"but remember we have formulae for integration which amounts to weighted sums of the function at different points! We can then expand the right hand side and write a General Linear Multistep formula:\n",
"\n",
"$$\n",
"\\sum_{j=0}^{s} \\alpha_j y_{i+j} = h \\sum_{j=0}^{s} \\beta_j f(t_{i+j}, y_{i+j})\n",
"$$\n"
]
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"source": [
"where the $\\alpha_j$ and $\\beta_j$ coefficients are chosen for accuracy and balance of computation. Note that this indexing is a matter of stype; in general we are interested in the final solution $y_{i+s}$, and $\\alpha_s=1$ as a matter of normalization and convenience."
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "LyPp-R3LFf7G"
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"source": [
"##Explicit linear multistep methods"
]
},
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"cell_type": "markdown",
"metadata": {
"id": "-JxmsBfPFtf9"
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"source": [
"When $\\beta_s = 0$, the final solution, $y_i+s$ depends only on previous solutions and is therefore explicit.\n",
"\n",
"This scheme is often used to generate a *predictor* based solely on what has happened before. While a good guess, it must be *corrected* using some kind of scheme like Heun's method in order to capture anything that happened during the interval.\n",
"\n",
"This scheme does not handle unevenly spaced steps (a significant shortfall!), and doesn't self-start. Moreover, explicit single-step methods generally outperform these, and they are seldom used."
]
},
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"metadata": {
"id": "lGdxGW9bHMSo"
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"source": [
"## Backward Difference Formulae: Implicit linear multistep methods"
]
},
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"source": [
"If we say $\\beta_{j\\ne s}=0$, we arrive at the implicit linear multistep method, better known as the Backward Difference Formulae which is the default for many modern computational tools.\n",
"\n",
"Starting from: $\\frac{dy}{dx} = f(x,y)$, the $\\alpha_j$ coefficients are found from the derivative of a Lagrange interpolation polynomial fit to the distory: $ ... $.\n",
"\n",
"The first 5 orders are:\n",
"\n",
"$$ \\begin{align}\n",
"y_{n+1}^{(1)} &= y_n + h f(x_{n+1}, y_{n+1})\\\\\n",
"y_{n+1}^{(2)} &= \\frac{4}{3} y_n - \\frac{1}{3} y_{n-1} + \\frac{2}{3} h f(x_{n+1}, y_{n+1})\\\\\n",
"y_{n+1}^{(3)} &= \\frac{18}{11} y_n - \\frac{9}{11} y_{n-1} + \\frac{2}{11} y_{n-2} + \\frac{6}{11} h f(x_{n+1}, y_{n+1})\\\\\n",
"y_{n+1}^{(4)} &= \\frac{48}{25} y_n - \\frac{36}{25} y_{n-1} + \\frac{16}{25} y_{n-2} - \\frac{3}{25} y_{n-3} + \\frac{12}{25} h f(x_{n+1}, y_{n+1})\\\\\n",
"y_{n+1}^{(5)} &= \\frac{300}{137} y_n - \\frac{300}{137} y_{n-1} + \\frac{120}{137} y_{n-2} - \\frac{25}{137} y_{n-3} + \\frac{12}{137} y_{n-4} + \\frac{60}{137} h f(x_{n+1}, y_{n+1})\n",
"\\end{align}\n",
"$$\n",
"\n",
"Note that the Backward Euler method is BDF1.\n",
"\n",
"The benefits of BDFs are:\n",
"* There is no requirement for a constant step size\n",
"* It is implicit and therefore good for stiff equations\n",
"* One can dynamically change between orders to self-start and restart if the physics change."
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "h2vx-1xcKwIn"
},
"source": [
"#Summary of initial value problems"
]
},
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"id": "iTp36ddzK9Ot"
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"source": [
"Explicit methods:\n",
"* Easy to calculate.\n",
"* Parallelize well.\n",
"* Suffer from numerical instability.\n",
"* Require small step sizes for stiff equations.\n",
"\n",
"Implicit methods:\n",
"* Computationally intensive (general require root finding / linear systems).\n",
"* Don't parallelize well.\n",
"* Are much more numerically stable.\n",
"* Can take *significantly* larger step sizes without diverging.\n",
"\n",
"Systems of equations are natural and ready extensions of the methods.\n",
"\n",
"Reduction of order can be applied to higher order derivatives.\n",
"\n",
"Adaptive time stepping is very important and can be achieved through clever (or brute force) methods without much additional expense.\n",
"\n",
"The explicit Runge-Kutta methods efficiently achieve accurate estimates if numerical instability isn't a factor.\n",
"\n",
"Implicit RK methods require simultaneous solutoin of several equations which can exponenetially increase the computaitonal cost.\n",
"\n",
"Explicit linear multistep methods have conditions which make them impractical.\n",
"\n",
"Implicit linear multistep (Backward Differential Formulas: BDF) methods have excellent properties while exploiting the solution history."
]
},
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"metadata": {
"id": "wNYqZIKQNKln"
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"source": [
"# Dr. Mike's tips:\n",
"\n",
"* Know your physics. If you don't, go with an adaptive BDF method (the default of most software).\n",
"* If you know your system is not stiff, RK45 is the go-to and you will substantially benefit in computer time.\n",
"* If you know your physics has abrupt changes (e.g.: steps / pulses) consider keeping with Backward Euler - no higher-order accuracy is possible. "
]
}
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\n",
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{
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\n",
"text/plain": ""
},
"metadata": {},
"output_type": "display_data"
}
]
}
},
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],
"_model_module": "@jupyter-widgets/controls",
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],
"layout": "IPY_MODEL_10335579eb014090a5606eecffdc10a0"
}
}
}
}
},
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"nbformat_minor": 0
}