{ "cells": [ { "cell_type": "code", "execution_count": 8, "metadata": { "slideshow": { "slide_type": "skip" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "C:\\Anaconda3\\lib\\site-packages\\IPython\\core\\magics\\pylab.py:160: UserWarning: pylab import has clobbered these variables: ['beta', 'f']\n", "`%matplotlib` prevents importing * from pylab and numpy\n", " \"\\n`%matplotlib` prevents importing * from pylab and numpy\"\n" ] } ], "source": [ "%pylab inline\n", "lecture = 11" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "#Lecture 11: Numerical Methods for Ordinary Differential Equations\n", "\n", "## Topics\n", "\n", "* I. Introduction\n", " * Picard's Theorem \n", " \n", "* II. Examples in Finance\n", " * Black-Scholes Equation\n", " * Affine Term-structure model\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "* III. Numerical Methods\n", " * Finite Difference Methods\n", " * The Euler's Methods\n", " * Consistency, Stability and Convergence\n", " * The Backward Euler's Methods\n", " * The Crank-Nicholson Method\n", " * The Runge-Kutta Method\n", " \n", "* IV. Numerical Examples in Python\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# I. Introduction\n", "\n", "\n", "* The initial value problem (IVP) of a general **first** order ordinary differential equation (ODE) \n", "\n", "$$\n", "y' = f(t,y), \\;\\; y(t_0) = y_0\n", "$$\n", "\n", "* The integral formulation\n", "\n", "$$\n", "y(t) = y_0 + \\int_{t_0}^t f(s,y(s)) \\; ds\n", "$$\n", "\n", "* If $f(t,y)$ is independent of $y$, solving the ODE is simply an integration. \n", "\n", "* In general, the integral equation is not any easier to solve.\n", "\n", "* If $f(t,y)$ is independent of $t$, the ODE is said to be **autonomous**\n", "\n", "\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "* If $y$ and $f$ are vectors, this becomes a system of first order ODEs\n", "\n", "$$\n", "\\renewcommand{bs}{\\boldsymbol}\n", "\\renewcommand{by}{\\boldsymbol{y}}\n", "\\renewcommand{bf}{\\boldsymbol{f}}\n", "\\by' = \\bf(t, \\by), \\;\\; \\by(t_0) = \\by_0\n", "$$\n", "\n", "* General $n^{th}$ order ODE\n", "\n", "$$\n", "y^{(n)}(t) = f(t,y(t),y'(t), \\cdots, y^{(n-1)}(t))\n", "$$\n", "\n", "* Can be converted into a system of first order ODEs\n", "\n", "$$\n", "\\bs{z}' = \\bs{g}(t, \\bs{z})\n", "$$\n", "\n", "$\\hspace{0.3in}$ where \n", "\n", "$$\n", "\\begin{matrix}\n", "\\bs{z} = \\left[\n", "\\begin{matrix}\n", "y(t) \\\\\n", "y'(t) \\\\\n", "\\vdots \\\\\n", "y^{(n-1)}(t) \n", "\\end{matrix}\n", "\\right], \\;\\; \\mbox{and} \\;\\;\n", "\\end{matrix}\n", "\\begin{matrix}\n", "\\bs{g}(t, \\bs{z}) = \\left[\n", "\\begin{matrix}\n", "y'(t) \\\\\n", "y''(t) \\\\\n", "\\vdots \\\\\n", "y^{(n-1)}(t) \\\\\n", "f(t,y(t),y'(t), \\cdots, y^{(n-1)}(t))\n", "\\end{matrix}\n", "\\right]\n", "\\end{matrix}\n", "$$\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Picard's Theorem\n", "\n", "* Interesting things one want to know about the IVP of the general first order systems of ODE:\n", "\n", " * 1) Is there a solution?\n", "\n", " * 2) Is the solution unique?\n", "\n", " * 3) Is the solution sensitive to the data?\n", "\n", " * 4) How to solve for the solution?\n", " \n", "\n", "* **Picard's theorem**:\n", "If $f(t,y)$ is **Lipschitz continuous** in $y$ in a neighborhood of $(t_0, y(t_0))$, then the IVP of the ODE has a unique solution in the neighborhood.\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# II. Examples in Finance\n", "\n", "### **Black-Scholes** equation\n", "\n", "$$\n", "C_t = \\frac{1}{2}\\sigma^2S^2C_{SS} + rSC_S - rC\n", "$$\n", "\n", "Define the Laplace transform of option price function $C(t,S)$ as\n", "\n", "$$\n", "\\renewcommand{hC}{\\hat{C}}\n", "\\hC(z,\\cdot) := \\mathcal{L}[C](z) = \\int_{0}^{\\infty}C(t,\\cdot)e^{-zt} \\; dt\n", "$$\n", "\n", "Taking the Laplace transform of the Black-Scholes equation,\n", "\n", "$$\n", "z\\hC = \\frac{1}{2}\\sigma^2S^2 \\hC_{SS} + rS \\hC_S - r \\hC + C_0\n", "$$\n", "\n", "Here $C_0$ is the time reversed payoff condition (*).\n", "\n", "So one way to solve Black-Scholes is to solve an ODE and then invert the Laplace Transform.\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "\n", "### Affine Term Structure model\n", "\n", "Assume the short rate is affine under the risk-neutral measure\n", "\n", "$$\n", "dr_t = \\kappa(\\theta-r_t)dt + \\sqrt{\\sigma_1 +\\sigma_2 r_t}\\;dW_t\n", "$$\n", "\n", "Then bond prices are solution to the PDE:\n", "\n", "$$\n", "\\frac{1}{2}P_{rr}(\\sigma_1 +\\sigma_2 r) + P_r\\kappa(\\theta - r)+ P_t -rP = 0\n", "$$\n", "\n", "with $P(T,T) = 1$. Looking for solution in the form \n", "\n", "$$\n", "P(r,t,T) = e^{A(T-t) - B(T-t)r},\n", "$$\n", "\n", "we find that $A(\\cdot), B(\\cdot)$ solve the following system of ODE\n", "\n", "\\begin{aligned}\n", "-B' & = \\frac{1}{2}\\sigma_2B^2 + \\kappa B - 1\n", "\\\\\n", " A' & = \\frac{1}{2}\\sigma_1B^2 - \\kappa \\theta B\n", "\\end{aligned}\n", "with $A(0) = B(0) = 0$.\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# III. Numerical Methods \n", "\n", "* Will focus on **Finite Difference Methods**(FDM) here.\n", "\n", "\n", "* Other methods for ODE/PDEs: Finite element methods, Spectral Methods, etc.\n", "\n", "\n", "* All methods for IVP of ODE are recursions that generate $y^{n+1}$ from previous $y^n$ together with evaluating the function $f(t, y)$ a few times around $t^n$.\n", "\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "\n", "## Finite Difference Methods(FDM)\n", "\n", "Employing finite difference method typically means:\n", "\n", "1) Generate a grid of points $(t_k, y_i)$ where we want to find the solutions\n", "\n", "2) Substitute the derivatives in ODE/PDE with finite difference schemes, which converts the ODE/PDE into a system of algebraic equations.\n", "\n", "3) Solve the system of algebraic equations.\n", "\n", "4) Implement and debug the compute code.\n", "\n", "5) Perform sanity check, error analysis, sensitivity analysis, etc, by any available means: intuitively, analytically or numerically.\n", "\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## The Euler's Method \n", "\n", "* Approximate the first derivative by the forward difference formula\n", "\n", "$$\n", "\\mathcal{D}_+y(t) = \\frac{y(t+h)-y(t)}{h} = y'(t) + O(h)\n", "$$\n", "\n", "* The one step (forward) Euler's method:\n", "\n", "$$\n", "\\frac{y^{n+1} - y^n}{h} = f(t^n, y^n);\n", "$$\n", "\n", "* or\n", "\n", "$$\n", "y^{n+1} = y^n + h f(t^n, y^n).\n", "$$\n", "\n", "* The method is **explicit**, we do not need to solve any equations.\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Consistency, Stability and Convergence\n", "\n", "* For any FDM that are employed to solve practical problems, we should ask\n", "\n", " * 1) How accurate is the method?\n", " * 2) Does it converge?\n", " * 3) What is the best choice of step sizes?\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Local Truncation Error \n", "\n", "* Defined as the amount by which the exact solution does not satisfy the numerical scheme.\n", "\n", "\n", "* Just plug the exact values of the functions/variable into the FDM scheme and calculate the error, for Euler scheme, this is,\n", "\n", "\n", "\\begin{aligned}\n", "\\small\n", "\\mathcal{N}_h y(t^n) & = y(t^{n+1}) - y(t^n) - h f(t^n, y(t^n))\n", "\\\\\n", " & = y(t^{n}+h) - y(t^n) - h f(t^n, y(t^n))\n", "\\\\\n", " & = \\left( y(t^n) + hy'(t^n) + \\frac{h^2}{2}y''(t^n)+ \\cdots \\right) - y(t^n) - h f(t^n, y(t^n))\n", "\\\\\n", " & = \\frac{h^2}{2}y''(t^n) + O(h^3).\n", "\\end{aligned}\n", "\n", " $\\\\$ where we used the exact ODE equation $y'(t^n) = f(t^n, y(t^n))$.\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Consistency \n", "\n", "* An FDM is **consistent** if the local truncation error goes to 0 as the step size goes to 0.\n", "\n", "\n", "* An FDM is **consistent with order $q>1$** if $|\\mathcal{N}_h y(t^n) | = O(h^q)$.\n", "\n", "\n", "* The Euler method is consistent with the second order.\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### \"Consistently Insufficient\"\n", "\n", "* Turns out being consistent is not enough.\n", "\n", "\n", "* Consider the model (for analyzing stability) ODE\n", "$$\n", "y'(t) = \\lambda y(t), \\; y(0) = 1.0, \\; \\lambda < 0.\n", "$$\n", "\n", "\n", "* Applying the Euler's method, gives:\n", "\n", "$$\n", "y^{n+1} = y^n + \\lambda y^n h = ( 1 + \\lambda h) y^n = ( 1 + \\lambda h)^2 y^{n-1} = \\cdots \\bs{\\leadsto}\n", "$$\n", "$$\n", "y^n = ( 1 + \\lambda h)^n \n", "$$\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "\n", "* The solution will explode if $|1+\\lambda h| > 1$. For example, when $\\lambda = -10$ and $h = 0.25$.\n", "\n", "\n", "* While the exact solution of the problem is $y(t) = e^{\\lambda t}$, which decays exponentially with $\\lambda <0$.\n", "\n", "\n", "* The problem is with error propagation of the FDM, we need more..." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Stability\n", "\n", "* We need one more property: **zero-stability**\n", "\n", "\n", "* A method is called **zero-stable ** if there are constants $h_0$ and $K$ so for any mesh functions $y_h$ and $z_h$ on an interval $[0,T]$ with $h \\leq h_0$,\n", "\n", "$$\n", "|y^n - z^n| \\leq K |y^0 - z^0| \n", "$$\n", "or the weaker version\n", "$$\n", "|y^n - z^n| \\leq K\\left\\{ |y^0 - z^0| + \\max_{1 \\leq j \\leq N} | \\mathcal{N}_h y(t^j) - \\mathcal{N}_h z(t^j) | \\right\\}\n", "$$\n", "for $1 \\leq n \\leq N$.\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "\n", "* Zero-stability essentially says errors (e.g. roundoff errors, function evaluation errors) introduced in any step does not get magnified later on.\n", "\n", "\n", "* One-step FDM can be shown to be zero-stable given sufficiently small step size and if $f$ is Lipschitz continuous in $y$." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Consistency + Stability = Convergence\n", "\n", "* An FDM is said to be **convergent with order $p > 0$ **, or to have the order of accuracy $p$, if for any finite $T$ for which the ODE has a solution,\n", "\n", "$$\n", "|y^n - y(t^n)| = O(h^p), \\;\\; \\forall 0 \\leq n \\leq T/h.\n", "$$\n", "\n", "\n", "* A central theorem in numerical method for differential equations is the **Lax equivalence theorem**: $\\;\\;$Any consistent method is convergent if and only if it is zero-stable or\n", "\n", "$$\n", "\\mbox{consistency + stability = convergence}\n", "$$\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "\n", "* For the Euler method, the stability can be satisfied if the time step satisfies the **stability criterion**\n", "\n", "$$\n", "|1+\\lambda h| \\leq 1 \\Longrightarrow 0 < h < -\\frac{2}{\\lambda }.\n", "$$\n", "\n", "\n", "* This condition is often referred to as the **CFL (Courant-Friedrichs–Lewy)** condition." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Absolute Stability\n", "\n", "* The Euler's method is said to be **conditionally stable**.\n", "\n", "\n", "* Its **region of absolute stability** is defined as the set of complex numbers $z = \\lambda h$, such that the FDM solution decays to 0, that is\n", "\n", "$$\n", "|1+\\lambda h| = |1+z| = |z - (-1)| \\leq 1,\n", "$$\n", "\n", "amounts to a unit disk with radius 1 and center $(-1,0)$.\n", "\n", "\n", "* An FDM is called **A-Stable** or **unconditionally stable** if its region of absolute stability is the entire negative left half plan, i.e. $\\Re{z} < 0$.\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## The backward Euler's Method \n", "\n", "* The one step backward Eulers method:\n", "\n", "$$\n", "\\frac{y^{n+1} - y^n}{h} = f(t^{n+1}, y^{n+1})\\; \\Longrightarrow \\;\n", "y^{n+1} = y^n + h f(t^{n+1}, y^{n+1}).\n", "$$\n", "\n", "* The method is **implicit**: if $f(t,y)$ is nonlinear, we would have to solve a nonlinear equation to get $y^{n+1}$.\n", "\n", "* The local truncation error is\n", "\n", "\\begin{aligned}\n", "\\mathcal{N}_h y(t^n) & = y(t^{n+1}) - y(t^n) - h f(t^{n+1}, y(t^{n+1}))\n", "\\\\\n", " & = y(t^{n+1}) - y(t^{n+1}-h) - h f(t^{n+1}, y(t^{n+1}))\n", "\\\\\n", " & = -\\frac{h^2}{2}y''(t^{n+1}) + O(h^3).\n", "\\end{aligned}\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "\n", "* Set $f(t,y) = \\lambda y$, then \n", "\n", "$$\n", "y^{n+1} = y^n + h\\lambda y^{n+1}, \\Longrightarrow y^{n+1} =\\frac{1}{1-h\\lambda}y^n\n", "$$\n", "\n", "* The CFL condition is $\\frac{1}{1-h\\lambda} \\leq 1$, which is always satisfied with $h > 0, \\lambda < 0$, so it is A-Stable." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## The Crank-Nicholson Method \n", "\n", "* Both Euler's method are of first order, Crank-Nicholson (also called **Trapezoidal method**) is second order:\n", "\n", "$$\n", "\\frac{y^{n+1} - y^n}{h} = \\frac{1}{2}\\left( f(t^n, y^n) + f(t^{n+1}, y^{n+1}) \\right)\\; \\Longrightarrow \\;\n", "$$\n", "$$\n", "y^{n+1} = y^n + \\frac{h}{2}\\left( f(t^n, y^n) + f(t^{n+1}, y^{n+1}) \\right).\n", "$$\n", "\n", "* The local truncation error is\n", "\n", "\\begin{aligned}\n", "\\mathcal{N}_h y(t^n) & = y(t^{n+1}) - y(t^n) - \\frac{h}{2}\\left( f(t^n, y^n) + f(t^{n+1}, y^{n+1}) \\right).\n", "\\\\\n", " & = -\\frac{h^3}{6}y'''(t^{n+1/2}) + O(h^4).\n", "\\end{aligned}" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "* Set $f(t,y) = \\lambda y$,\n", "\n", "$$\n", "y^{n+1} =\\frac{1+h\\lambda}{1-h\\lambda}y^n\n", "$$\n", "\n", "\n", "* The CFL condition is $|\\frac{1+h\\lambda}{1-h\\lambda} |\\leq 1$, which is always satisfied with $h > 0, \\lambda < 0$, so it is also unconditionally stable." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## The Runge-Kutta Method \n", "\n", "* The Crank-Nicholson method is implicit, to make it explicit, we can approximate $y^{n+1}$ in right hand side using the forward Euler's method, and this gets us to the simplest explicit Runge-Kutta method (usually called the Heun's method)\n", "\n", "\\begin{aligned}\n", "y^* & = y^n + h f(t^n, y^n)\n", "\\\\\n", "y^{n+1} & = y^n + \\frac{h}{2}\\left( f(t^n, y^n) + f(t^{n+1}, y^*) \\right).\n", "\\end{aligned}\n", "\n", "* The method is second order, but only conditionally stable.\n", "\n", "* The is an example of a powerful class of mulit-step methods called **predictor-corrector** methods: the forward Euler as the predictor and the Crank-Nicholson is the corrector." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "\n", "* The classical Runge-Kutta scheme is the RK4, based on Simpson's integral formula\n", "\n", "\\begin{aligned}\n", "K_0 & = f(t^n, y^n)\n", "\\\\\n", "K_1 & = f(t^n + \\frac{h}{2}, y^n + \\frac{h}{2} K_0)\n", "\\\\\n", "K_2 & = f(t^n + \\frac{h}{2}, y^n + \\frac{h}{2} K_1)\n", "\\\\\n", "K_3 & = f(t^n + h, y^n + hK_2)\n", "\\\\\n", "y^{n+1} & = y^n + \\frac{h}{6}\\left( K_0 + 2K_1 + 2K_2 + K_3 \\right).\n", "\\end{aligned}\n", "\n", "* The method is fourth-order accurate and conditionally stable.\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Stiff ODEs\n", "\n", "* ODEs with rapidly decaying transients or with varying time scales often presents huge problems for numerical methods which are not A-Stable.\n", "\n", "* Example:\n", "$$\n", "y'(t) = -50[y(t) - t] + 1, \\;\\; y(0) = 1;\n", "$$\n", "\n", "\n", "* The solution to the problem can be found exactly: $y(t) = e^{-50t} + t$. It has a slow varying part $t$ and a rapidly decaying part $e^{-50t}$.\n", "\n", "\n", "* Using the explicit Euler's method requires a time step $h<2/50 = 0.04 << 1$, i.e. many time steps before reaching the reasonable solution." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "\n", "* In the homework, you will encounter another example, where in a system of first order ODEs, different components of the solution behave in a very different time scales, and the fast changing one dominates the step size in order for the scheme to be stable.\n", "\n", "\n", "* For stiff ODEs, you either choose really small step size with explicit method (very inefficient!) or choose an A-Stable method (it will cost more in each step)." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# IV. Numerical Examples in Python\n", "\n", "* scipy.integrate contains a collection of ODE solvers: mostly wrapped around the matured software package ODEPACK (A Fortran ODE solver package). New updates are available (please check).\n", "\n", "* Integrating \"Van der Pol Oscillator\" using odeint in scipy:\n", "\n", "\n", "\n" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib\n", "from scipy.integrate import odeint\n", "\n", "r = 0.1\n", "def f(y,t):\n", " return [y[1], r*(1 - y[0]*y[0])*y[1] - y[0]]\n", "\n", "# initial value\n", "y0 = [2.0, 1.]\n", "\n", "n = 10000\n", "T = 3.0*r\n", "h = T/n\n", "# print h\n", "ts = np.arange(0.0001,T, h)\n", "ys = odeint(f, y0, ts)\n", " \n", "fig = figure(figsize=[12, 4])\n", "subplot(1, 2, 1)\n", "plot(ts, ys[:, :], '.-') \n", "xlabel('Time')\n", "title('odeint')\n", "\n", "ax = fig.add_subplot(122)\n", "ax.set_axis_off()\n", "ax.text(0, .5, \"$\\;\\; y' = \\mu (1-x^2)y - x$ \", size=\"xx-large\");\n", "ax.text(0, .6, \"$\\;\\; x' = y$\", size=\"xx-large\");\n", "ax.text(0, .75, \"Integrating Van der Pol system\", size=\"x-large\");\n", "\n", "show()\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "\n", "* Integrating lorenz system using ode(*) in scipy\n", "* The lorenz system describing the atmospheric convection: chaotic but resembles a beautiful butterfly \n", "\n", "\n" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from scipy.integrate import ode\n", "from mpl_toolkits.mplot3d import Axes3D\n", "\n", "def lorenz_sys(t, q):\n", " x = q[0]\n", " y = q[1]\n", " z = q[2]\n", " # sigma, rho and beta are global.\n", " f = [sigma * (y - x),\n", " rho*x - y - x*z,\n", " x*y - beta*z]\n", " return f\n", "\n", "\n", "#ic = [1.0, 2.0, 1.0]\n", "ic = [0.01, 0.01, 0.01]\n", "t0 = 0.0\n", "t1 = 70.0\n", "dt = 0.01\n", "\n", "sigma = 10.0\n", "rho = 28.0\n", "beta = 8.0/3.0\n", "\n", "#sigma = 28.0\n", "#rho = 46.92\n", "#beta = 4.0\n", "\n", "solver = ode(lorenz_sys)\n", "\n", "t = []\n", "sol = []\n", "solver.set_initial_value(ic, t0)\n", "#solver.set_integrator('dop853')\n", "solver.set_integrator('dopri5')\n", "\n", "while solver.successful() and solver.t < t1:\n", " solver.integrate(solver.t + dt)\n", " t.append(solver.t)\n", " sol.append(solver.y)\n", "\n", "t = array(t)\n", "sol = array(sol)\n", "\n", "fig = figure()\n", "ax = Axes3D(fig)\n", "ax.plot(sol[:,0], sol[:,1], sol[:,2])\n", "xlabel('x')\n", "ylabel('y')\n", "\n", "ax = fig.add_subplot(122)\n", "ax.set_axis_off()\n", "ax.text(2, .3, \"$\\;\\; z' = x y -\\kappa z$\", size=\"xx-large\");\n", "ax.text(2, .4, \"$\\;\\; y' = x ( \\gamma - z ) - y $\", size=\"xx-large\");\n", "ax.text(2, .5, \"$\\;\\; x' = \\sigma (y - x) $\", size=\"xx-large\");\n", "ax.text(2, .65, \"Integrating Lorenz system\", size=\"x-large\");\n", "\n", "show()\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# Summary \n", "\n", "* ODE basics\n", "* Examples in Finance\n", "* Details of the most basic numerical methods\n", "* Consistency, Stability and Convergence\n", "* Stability region and stiffness\n", "* The Runge-Kutta and multi-step methods \n", "* Numerical Examples in Python\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# Homework \n", "\n", "* Applying the forward Euler's scheme to the second order ODE:\n", "\n", "$$\n", "y'' + (\\lambda+1)y' + \\lambda y = 0, \\;\\; y(0) = 1, \\;\\; y'(0) = \\lambda - 2, \\;\\; \\lambda >> 1.\n", "$$\n", "\n", "Rewrite it as a system of first order ODEs. Find the region of absolute stability. (Hint: find the eigenvalue decomposition of the coefficient matrix, and the region of absolute stability is the domain where the step size is chosen so that each eigen value satisfies the condition for the 1D ODE.)\n", "\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# Reference\n", "\n", "* J. Stoer and R. Bulirsch, Chapter 7 of Introduction to Numerical Analysis, Second Edition, Springer, 1993." ] } ], "metadata": { "celltoolbar": "Slideshow", "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": "3.6.5" } }, "nbformat": 4, "nbformat_minor": 1 }