{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "# Import libraries\n", "import time\n", "import numpy as np\n", "from numpy import linalg as LA\n", "\n", "import matplotlib.pyplot as plt\n", "plt.rcParams['text.usetex'] = True" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## MA934\n", "\n", "## Solving (differential) equations" ] }, { "cell_type": "markdown", "metadata": { "cell_style": "split", "slideshow": { "slide_type": "slide" } }, "source": [ "### Root-finding in 1D\n", "\n", "Task: find $x$ such that $f(x) = 0$.\n", "\n", "Interval $[a_0,b_0]$ brackets a root of $f(x)$ if $f(a_0)\\,f(b_0) <0$.\n", "\n", "Bracket and bisect method:\n", "\n", "1 $c_n = \\frac{1}{2}(a_n+b_n)$ \n", "2 If $f(a_n)\\,f(c_n) <0$, $[a_{n+1}, b_{n+1}] = [a_n, c_n]$. Otherwise $[a_{n+1}, b_{n+1}] = [c_n, b_n]$ \n", "3 Repeat until $\\epsilon_n = b_n-a_n < \\epsilon_\\text{tol}$." ] }, { "cell_type": "markdown", "metadata": { "cell_style": "split" }, "source": [ "Convergence: $\\epsilon_n \\sim 2^{-n}$." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Root-finding in 1D: Newton-Raphson iteration\n", "\n", "Suppose root is at $x=x^*$ and current estimate is $x_n$.\n", "\n", "Write $x_{n+1} = x_n+\\delta_n$ and try to choose $\\delta_n$ such that\n", "$f(x_{n+1}) = 0$:\n", "\n", "Taylor expand:\n", "$$\n", "0 = f(x_{n+1}) = f(x_n + \\delta_n) = f(x_n) + \\delta_n\\,f^\\prime(x_n) + \\mathcal{O}(\\delta_n^2) \n", "$$\n", "Assuming we are near the root, we neglect the $\\mathcal{O}(\\delta_n^2)$ terms and solve for $\\delta_n$: \n", "$$\n", "\\delta_n = -\\frac{f(x_n)}{f^\\prime(x_n)}.\n", "$$\n", "This gives the Newton-Raphson iterative method:\n", "$$\n", "x_{n+1} = x_n -\\frac{f(x_n)}{f^\\prime(x_n)}.\n", "$$" ] }, { "cell_type": "markdown", "metadata": { "cell_style": "split", "slideshow": { "slide_type": "slide" } }, "source": [ "### Convergence properties of Newton-Raphson\n", "\n", "Geometrical interpretation:\n", "\n", "\"NR\" " ] }, { "cell_type": "markdown", "metadata": { "cell_style": "split" }, "source": [ "NR is not guaranteed to converge:\n", "\n", "\n", "\n", "\"NR\" \n", "\n", "\n", "\n", "\"NR\" " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Super-exponential convergence of Newton-Raphson\n", "\n", "When NR does converge, it converges super-exponentially.\n", "\n", "Let $\\epsilon_n = x_n - x_*$. Then NR formula gives:\n", "$$\n", "\\epsilon_{n+1} = \\epsilon_n - \\frac{f(x^*+\\epsilon_n)}{f^\\prime(x^*+\\epsilon_n)}.\n", "$$\n", "Taylor expanding and using $f(x^*)=0$ one obtains (check):\n", "\n", "$$\n", "\\begin{align*}\n", "f(x^*+\\epsilon_n) &= \\epsilon_n\\, f^\\prime(x_*)\\,\\left( 1+ \\frac{\\epsilon_n}{2}\\frac{f^{\\prime\\prime}(x_*)}{f^\\prime(x_*)} \\right) + O(\\epsilon_n^3),\\\\\n", "f^\\prime(x^*+\\epsilon_n) &= f^\\prime(x_*)\\, \\left( 1+ \\epsilon_n \\frac{f^{\\prime\\prime}(x_*)}{f^\\prime(x_*)} \\right) + O(\\epsilon_n^2).\n", "\\end{align*}\n", "$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Super-exponential convergence of Newton-Raphson\n", "\n", "Keeping only the leading order terms on the RHS, there is a cancellation at $\\mathcal{O}(\\epsilon_n)$ and we get\n", "$$\n", " \\epsilon_{n+1} = \\alpha\\,\\epsilon _n^2.\n", "$$\n", "where $\\alpha = \\frac{f^{\\prime\\prime}(x_*)}{2\\,f^\\prime(x_*)}$ depends on the properties of $f$ at the root, $x^*$.\n", "\n", "This nonlinear recursion relation can be linearised by $a_n = \\log_\\alpha \\epsilon_n$ to give:\n", "$$\n", "a_{n+1} = 2\\,a_n+1\n", "$$\n", "Solution is $a_n = c_0\\,2^{n-1}-1$ where $c_0$ is a constant. \n", "In original variables, choosing $c_0$ to match the initial condition, $\\epsilon_0$, we get\n", "$$\n", "\\epsilon_n = \\epsilon_0\\,\\left|\\alpha \\right|^{-1}\\,\\left|\\alpha \\right|^{2^n}.\n", "$$\n" ] }, { "cell_type": "markdown", "metadata": { "cell_style": "split", "slideshow": { "slide_type": "slide" } }, "source": [ "### Newton-Raphson in $\\mathbb{R}^n$\n", "\n", "System of $n$ equations in $\\mathbb{R}^n$:\n", "$$\n", "\\begin{align*}\n", "F_1(x_1\\ldots x_n) &= 0 \\\\\n", "\\vdots\\hspace{1.0cm} & \\ \\ \\vdots\\\\\n", "F_n(x_1\\ldots x_n) &= 0. \n", "\\end{align*}\n", "$$\n", "or \n", "$$\n", "\\mathbf{F}(\\mathbf{x}) = 0.\n", "$$\n", "\n", "As before, write $\\mathbf{x}_{n+1}=\\mathbf{x}_n+\\boldsymbol{\\delta}_n$ and try to choose $\\boldsymbol{\\delta}_n$ such that $\\mathbf{F}(\\mathbf{x}_{n+1})=0$." ] }, { "cell_type": "markdown", "metadata": { "cell_style": "split" }, "source": [ "Taylor expand:\n", "\n", "$$\n", "\\begin{align*}\n", "0 &= \\mathbf{F}(\\mathbf{x}_{n+1}) = \\mathbf{F}(\\mathbf{x}_n + \\boldsymbol{\\delta}_n)\\\\\n", "&= \\mathbf{F}(\\mathbf{x}_n) + \\mathbf{J}(\\mathbf{x}_n)\\,\\boldsymbol{\\delta}_n + \\mathcal{O}(\\left|\\boldsymbol{\\delta}\\right|_n^2) \n", "\\end{align*},\n", "$$\n", "\n", "where $\\mathbf{J}(\\mathbf{x}_n)$ is the Jacobian matrix\n", "\n", "$$\n", "\\mathbf{J}_{i\\,j} = \\frac{\\partial F_i}{\\partial x_j}(\\mathbf{x}_n).\n", "$$\n", "\n", "Neglecting the $\\mathcal{O}(\\left|\\boldsymbol{\\delta}_n\\right|^2)$ terms, we obtain $\\boldsymbol{\\delta}_n$ from a linear solve:\n", "\n", "$$\n", "\\boldsymbol{\\delta}_n = - \\mathbf{J}(\\mathbf{x}_n)\\,\\backslash \\, \\mathbf{F}(\\mathbf{x}_n)\n", "$$\n" ] }, { "cell_type": "markdown", "metadata": { "cell_style": "split", "slideshow": { "slide_type": "slide" } }, "source": [ "### Example: Newton-Raphson iteration in $\\mathbb{C}$.\n", "\n", "For complex valued functions of a complex variable:\n", "$$\n", "z_{n+1} = z_n - \\frac{f(z_n)}{f^\\prime(z_n)}\n", "$$\n", "\n", "Nonlinear iterated map which can lead to very rich dynamics (periodic cycles, chaos, intermittency etc). " ] }, { "cell_type": "markdown", "metadata": { "cell_style": "split" }, "source": [ "Example: compute basins of attraction in $\\mathbb{C}$ of the roots of the polynomial\n", "$$\n", "f(z) = z^3-1 =0.\n", "$$\n", "under NR iteration.\n", "\n", "\"NR\" " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Ordinary differential equations\n", "\n", "For initial value problems, it is generally sufficient to develop algorithms to solve autonomous first order systems in $\\mathbb{R}^n$: \n", "$$\n", "\\frac{d \\mathbf{u}}{d t}= \\mathbf{F}(\\mathbf{u}) \\hspace{0.5cm}\\text{with }\\hspace{0.5cm} \\mathbf{u}(0) = \\mathbf{U}_0.\n", "$$\n", "For example, the second order non-autonomous equation,\n", "$$\n", "\\frac{d^2 y}{d t^2} + 2 \\nu \\omega \\frac{d y}{d t} + \\omega^2 y = F(t),\n", "$$\n", "is equivalent (check) to this 3-dimensional autonomous system:\n", "$$\n", "\\frac{d }{d t} \\left(\n", "\\begin{array}{c}\n", "u^{(1)}\\\\ \n", "u^{(2)}\\\\ \n", "u^{(3)} \n", "\\end{array}\n", "\\right)\n", "= \n", "\\left(\n", "\\begin{array}{c}\n", "-2 \\nu \\omega u^{(1)} - \\omega^2 u^{(2)} + F(u^{(3)})\\\\ \n", "u^{(1)}\\\\ \n", "1 \n", "\\end{array}\n", "\\right)\n", "\\hspace{0.5cm}\\text{where }\\hspace{0.5cm} \\left(\n", "\\begin{array}{c}\n", "u^{(1)}\\\\ \n", "u^{(2)}\\\\ \n", "u^{(3)} \n", "\\end{array}\n", "\\right) = \\left(\n", "\\begin{array}{c}\n", "\\frac{d y}{d t}\\\\ \n", "y\\\\ \n", "t \n", "\\end{array}\n", "\\right).\n", "$$" ] }, { "cell_type": "markdown", "metadata": { "cell_style": "split", "slideshow": { "slide_type": "slide" } }, "source": [ "### Discretisation and time stepping\n", "\n", "**Discretisation**: approximate continuous $\\mathbf{u}(t)$ on $t\\in [0,T]$ by\n", "$\\{\\mathbf{u}_i\\ :\\ i=0\\ldots N\\}$. Here \n", "\n", "$$\n", "\\begin{align*}\n", "\\mathbf{u}_i &= \\mathbf{u}(t_i)\\\\\n", "t_i &=i\\,h,\n", "\\end{align*}\n", "$$\n", "\n", "and the \"time step\" is\n", "\n", "$$\n", "h=\\frac{T}{N}.\n", "$$" ] }, { "cell_type": "markdown", "metadata": { "cell_style": "split" }, "source": [ "If $h$ is \"small\" then\n", "\n", "$$\n", "\\frac{d \\mathbf{u}}{d t}= \\mathbf{F}(\\mathbf{u}) \\hspace{0.5cm}\\text{with }\\hspace{0.5cm} \\mathbf{u}(0) = \\mathbf{U}_0.\n", "$$\n", "\n", "can be hueristically approximated by\n", "\n", "$$\n", "\\frac{\\mathbf{u}_{i+1}-\\mathbf{u}_i}{h} = \\mathbf{F}(\\mathbf{u}_i)\n", "\\hspace{0.25cm}\\text{with }\\hspace{0.25cm} \\mathbf{u}_0 = \\mathbf{U}_0.\n", "$$\n", "\n", "Re-arranging, we get the (Forward Euler) time-stepping algorithm\n", "\n", "$$\n", "\\mathbf{u}_{i+1} = \\mathbf{u}_i + h\\,\\mathbf{F}_i \\hspace{0.25cm}\\text{with }\\hspace{0.25cm} \\mathbf{u}_0 = \\mathbf{U}_0,\n", "$$\n", "\n", "where $\\mathbf{F}_i$ means $\\mathbf{F}(\\mathbf{u}_i)$. " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Taylor's theorem\n", "\n", "\n", "If $f(x)$ is a real-valued function which is differentiable $n+1$ times on the interval $[x, x+h]$ then there exists a point, $\\xi$, in $[x, x+h]$ such that\n", "$$\n", "f(x+h) = f(x) + \\frac{1}{1!}\\, h \\, \\frac{d f}{d x}(x) + \\frac{1}{2!}\\, h^2 \\, \\frac{d^2f}{d x^2}(x) + \\ldots\\\\\n", "+ \\frac{1}{n!}\\, h^n \\, \\frac{d^nf}{d x^n}(x) + h^{n+1} R_{n+1}(\\xi)\n", "$$\n", "where\n", "$$\n", "R_{n+1}(\\xi) = \\frac{1}{(n+1)!} \\, \\frac{d^{n+1} f}{d x^{n+1}}(\\xi).\n", "$$\n", "Useful for systematic analysis of discrete approximations to derivatives and ODEs." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Finite difference approximations of derivatives\n", "\n", "Approximate $f^\\prime(x)$ by linear combinations of values of $f$ at nearby points. \n", "Taylor with $n=1$:\n", "$$\n", "f(x+h) = f(x) + h \\, f^\\prime(x) + \\mathcal{O}(h^2).\n", "$$\n", "Using same discrete notation as before, rearrange to get:\n", "$$\n", "f^\\prime(x_i) = \\frac{f_{i+1} - f_i}{h} +\\mathcal{O}(h). \\hspace{1.0cm}\\text{Forward difference formula.}\n", "$$\n", "Could also have started from $f(x-h)$ to obtain:\n", "$$\n", "f^\\prime(x_i) = \\frac{f_{i} - f_{i-1}}{h} +\\mathcal{O}(h). \\hspace{1.0cm}\\text{Backwards difference formula.}\n", "$$\n", "In both cases, the approximation error is $\\mathcal{O}(h)$." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Higher order finite differences: improving the error\n", "\n", "Improved accuracy can be obtained by linearly combining more points:\n", "\n", "$$\n", "\\begin{align*}\n", "f_{i+1} &= f_i + h\\,f^\\prime(x_i) + \\frac{1}{2}\\, h^2 \\, f^{\\prime\\prime}(x_i) + \\mathcal{O}(h^3)\\\\\n", "f_{i-1} &= f_i - h\\,f^\\prime(x_i) + \\frac{1}{2}\\, h^2 \\, f^{\\prime\\prime}(x_i) + \\mathcal{O}(h^3).\n", "\\end{align*}\n", "$$\n", "\n", "Take the linear combination $a_1\\,f_{i-1} +a_2\\,f_i +a_3\\,f_{i+1}$:\n", "\n", "$$\n", "a_1\\,f_{i-1} +a_2\\,f_i +a_3\\,f_{i+1} = (a_1+a_2+a_3)\\,f_i + (a_3-a_1)\\,h\\,f^\\prime(x_i)\\\\\n", "+ \\frac{1}{2}\\,(a_3+a_1)\\, h^2 \\, f^{\\prime\\prime}(x_i) + O(h^3).\n", "$$\n", "We want to choose the $a$'s to cancel the terms proportional to $h^0$ and $h^2$." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Higher order finite differences: improving the error\n", "\n", "$a_1$, $a_2$ and $a_3$ should therefore satisfy the equations\n", "\n", "$$\n", "\\begin{align*}\n", "a_1+a_2+a_3 &=0\\\\\n", "a_3-a_1 &= 1\\\\\n", "a_3+a_1 &=0.\n", "\\end{align*}\n", "$$\n", "\n", "We get $a_1=-\\frac{1}{2}$, $a_2=0$ and $a_3 = \\frac{1}{2}$.\n", "\n", "Rearranging to get an expression for $f^\\prime(x_i)$:\n", "$$\n", "f^\\prime(x_i) = \\frac{f_{i+1} - f_{i-1}}{2\\,h} + O(h^2). \\hspace{1.0cm}\\text{Centred difference formula.}\n", "$$\n" ] }, { "cell_type": "markdown", "metadata": { "cell_style": "split", "slideshow": { "slide_type": "slide" } }, "source": [ "### Higher order finite differences: improving the error\n", "\n", "The set of points underpinning a finite-difference approximation is known as the \"stencil\". \n", "\n", "A 5-point stencil leads to a 4th order accurate finite difference formula for $f^\\prime(x_i)$:\n", "\n", "$$\n", "\\frac{-f_{i+2}\\!+\\!8 f_{i+1}\\! - \\!8 f_{i-1}\\!+\\!f_{i-2}}{12\\,h}\\! +\\! O(h^4).\n", "$$\n" ] }, { "cell_type": "markdown", "metadata": { "cell_style": "split" }, "source": [ "\"FD\" \n", "\n", "Error as a function of $h$ for several finite difference approximations to the derivative of $f(x) = \\sqrt{x}$ at $x=2$\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Euler method again\n", "\n", "Return to the ODE (assumed scalar from now on)\n", "$$\n", "\\frac{d u}{d t}= F(u) \\hspace{0.5cm}\\text{with }\\hspace{0.5cm} u(0) = U_0.\n", "$$\n", "Accounting for the error in the forward difference approximation,\n", "\n", "$$\n", "\\frac{u_{i+1}-u_i}{h} +\\mathcal{O}(h) = F(u_i)\n", "\\hspace{0.25cm}\\text{with }\\hspace{0.25cm} u_0 = U_0.\n", "$$\n", "\n", "The Forward Euler time-stepping algorithm thus has *step-wise error* $\\mathcal{O}(h^2)$:\n", "\n", "$$\n", "u_{i+1} = u_i + h\\,F_i +\\mathcal{O}(h^2)\\hspace{0.25cm}\\text{with }\\hspace{0.25cm} \\mathbf{u}_0 = \\mathbf{U}_0,\n", "$$\n", "\n", "*Global error* is $\\mathcal{O}(N h^2) = T\\,\\mathcal{O}(h)$ since $h=\\frac{T}{N}$.\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Implicit methods: Backward Euler\n", "\n", "We could equally have used the backward difference approximation:\n", "\n", "$$\n", "\\frac{u_{i}-u_{i-1}}{h} +\\mathcal{O}(h) = F(u_i)\n", "\\hspace{0.25cm}\\text{with }\\hspace{0.25cm} u_0 = U_0.\n", "$$\n", "\n", "which gives (with $i \\to i+1$)\n", "\n", "$$\n", "u_{i+1} = u_i + h\\, F_{i+1} + O(h^2).\n", "$$\n", "\n", "This is called the Backward Euler method. Note $u_{i+1}$ appears on both sides. \n", "\n", "This is an example of an *implicit* method. Implicit methods require a Newton-Raphson solve at each timestep.\n" ] }, { "cell_type": "markdown", "metadata": { "cell_style": "split", "slideshow": { "slide_type": "slide" } }, "source": [ "### Improving accuracy: trapezoidal method\n", "\n", "Another way to think about time-stepping algorithms is via approximation of\n", "$$\n", "u(t+h) = u(t) + \\int_t^{t+h} \\!\\!\\!\\!F(u(\\tau))\\,d\\tau.\n", "$$\n", "\n", "Approximation of integral with left and right Riemann rule gives the forward and backward Euler methods respectively (check)." ] }, { "cell_type": "markdown", "metadata": { "cell_style": "split" }, "source": [ "If we use the Trapezoidal rule we get:\n", "\n", "$$\n", "u_{i+1} = u_i + \\frac{h}{2}\\left[F_i + F_{i+1} \\right].\n", "$$\n", "This is called the implicit trapezoidal method.\n", "\n", "The implicit trapezoidal method improves on the Euler methods because it has a stepwise error of $\\mathcal{O}(h^3)$. How to show this?" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Error analysis of timestepping rules\n", "\n", "Consider Taylor expansion of $u_{i+1}$:\n", "$$\n", "u_{i+1} = u_i + h \\frac{d u}{d t}(t_i) + \\frac{h^2}{2}\\frac{d^2 u}{d t^2}(t_i) + O(h^3)\\\\\n", "= u_i + h F_i +\\frac{1}{2} h^2 F_i\\, F^\\prime_i + O(h^3)\n", "$$\n", "Note the use of the chain rule:\n", "$$\n", "\\frac{d^2 u}{d t^2}(t_i) = \\left.\\frac{d }{d t}F(u(t))\\right|_{t=t_i} = \\left. F^\\prime(u(t))\\,\\frac{d u}{d t}\\right|_{t=t_i}\\\\\n", "= \\left. F^\\prime(u(t))\\,F(u(t))\\right|_{t=t_i} = F^\\prime_i\\,F_i.\n", "$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Error analysis of timestepping rules\n", "\n", "Idea: Taylor expand RHS of timestepping rule and identify the first order at which expansion differs from the above.\n", "\n", "$$\n", "\\begin{align*}\n", "F(u(t_{i+1})) &= F(u_i + h F_i + \\mathcal{O}(h^2))\\\\\n", "&= F(u_i) + (h F_i) \\frac{d F}{d u}(u(t_i)) + O(h^2)\\\\\n", "&=F_i + h F_i F_i^\\prime + O(h^2).\n", "\\end{align*}\n", "$$\n", "RHS of implicit trapezoidal method is therefore\n", "$$\n", "u_i + \\frac{h}{2}\\left[F_i + F_{i+1}\\right] = u_i + h F_i +\\frac{1}{2} h^2 F_i\\, F^\\prime_i + \\mathcal{O}(h^3)\n", "$$\n", "Comparing with $u_{i+1}$, stepwise error is $\\mathcal{O}(h^3)$." ] }, { "cell_type": "markdown", "metadata": { "cell_style": "split", "slideshow": { "slide_type": "slide" } }, "source": [ "### Predictor-corrector methods\n", "\n", "Can we get higher order accuracy with an explicit scheme?\n", "\n", "**Predictor-corrector** idea: use a less accurate explicit method to predict $u_{i+1}$ and then use the higher order formula to correct this prediction.\n", "\n", "Example: improved Euler method:" ] }, { "cell_type": "markdown", "metadata": { "cell_style": "split", "slideshow": { "slide_type": "-" } }, "source": [ "1. Use forward Euler as predictor:\n", "$$\n", "u^*_{i+1} = u_i + h F_i,\n", "$$\n", "and calculate\n", "$$\n", "F^*_{i+1} = F(u^*_{i+1}).\n", "$$\n", "2. Use the Trapezoidal Method to correct this :\n", "$$\n", "u_{i+1} = u_i + \\frac{h}{2}\\left[F_i + F^*_{i+1} \\right].\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Error analysis (similar to above - check) shows stepwise error is $\\mathcal{O}(h^3)$." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Choosing the timestep\n", "\n", "In practice we need to operate at a finite value of $h$. How do we choose it? \n", "\n", "Measure the error by comparing the numerical solution at a grid point, $\\widetilde{u}_i$, to the exact solution, $u(t_i)$. \n", "\n", "Two tolerance criteria are commonly used:\n", "$$\n", "\\begin{align*}\n", "&E_a(h) = \\left| \\widetilde{u}_i - u_i \\right| \\leq \\epsilon & \\text{Absolute error threshold,}\\\\\n", "&E_r(h) = \\frac{\\left| \\widetilde{u}_i - u_i \\right|}{\\left| u_i\\right|} \\leq \\epsilon & \\text{Relative error threshold.}\n", "\\end{align*}\n", "$$\n", "Fixing error tolerance allows us to take larger timesteps when the solution is varying slowly." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Adaptive timestepping : estimating error\n", "\n", "Problem: exact solution usually not known. Use trial steps:\n", "\n", "1. Take a trial step with stepsize $h$ from $u_i$ to get estimate $u^{\\rm B}_{i+1}$. \n", "2. Take 2 trial steps with stepsize $\\frac{h}{2}$ from $u_i$ to get estimate $u^{\\rm S}_{i+1}$. \n", "3. Estimate of local error is\n", "$$\n", "\\Delta = \\left|u^{\\rm B}_{i+1} - u^{\\rm S}_{i+1} \\right|.\n", "$$\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Adaptive timestepping : selecting the new stepsize\n", "\n", "If timestepping method is $n^{th}$ order, we know there is a constant $c$ such that\n", "\n", "$$\n", "c\\, h_{\\text{old}}^n = \\Delta.\n", "$$\n", "\n", "For maximum efficiency, we should choose $h_{\\text{new}}$ to saturate the error threshold:\n", "\n", "$$\n", "c\\,h_{\\text{new}}^n = \\epsilon.\n", "$$\n", "\n", "Eliminating $c$ between these two equations gives:\n", "\n", "$$\n", "h_{\\text{new}} = \\left(\\frac{\\epsilon}{\\Delta}\\right)^\\frac{1}{n}h_{\\text{old}}\n", "$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Stiff problems\n", "\n", "With adaptive stepsizing we expect to take larger timesteps when the solution is varying slowly and smaller timesteps when the solution is varying rapidly.\n", "\n", "Sometimes explicit methods result in very small step sizes even when the solution is varying *slowly*. Such problems are said to be *stiff*.\n", "\n", "Efficient solution of stiff problems requires bespoke stiff solvers that are usually implicit.\n", "\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Stiff problems\n", "\n", "Computational stiffness is a complicated topic: depends on the equation, the initial condition, the numerical method being used and the interval of integration. See [this article](http://www.scholarpedia.org/article/Stiff_systems).\n", "\n", "Common feature is that the solution is varying slowly but \"nearby\" solutions vary rapidly.\n", "\n", "The simple equation \n", "\n", "$$\n", "\\frac{d u }{d t} = -\\lambda\\, u \\hspace{0.5cm} \\text{with }u(0) = 1,\n", "$$\n", "\n", "turns out to have this property when $\\lambda \\gg 1$ or solution interval is long." ] }, { "cell_type": "markdown", "metadata": { "cell_style": "split", "slideshow": { "slide_type": "slide" } }, "source": [ "### Solving ODEs in Python\n", "\n", "[solve_ivp](https://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.solve_ivp.html) is a well developed system for solving systems of differential equations. In its basic form, it is very simple to use. \n", "\n", "Let's solve the *relaxation oscillator* equations:\n", "$$\n", "\\begin{align*}\n", "\\frac{d x}{d t} &= \\mu( y -(\\frac{1}{3} x^3 - x))\\\\\n", "\\frac{d y}{d t} &= -\\frac{1}{\\mu}x.\n", "\\end{align*}\n", "$$\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "cell_style": "split" }, "source": [ "**Steps**:\n", "\n", "1. Define the RHS of the system of equations.\n", "2. Integrate via ```solve_ivp```.\n", "3. Plot and analyse the solution." ] }, { "cell_type": "markdown", "metadata": { "cell_style": "split", "slideshow": { "slide_type": "slide" } }, "source": [ "### Step 1: define the RHS \n", "\n", "* ```fun``` (oscillator below) is the right hand side of the system (as a vector).\n", "* ```tspan``` is the interval of integration (t0, tf).\n", "* ```y0``` as the initial state/condition.\n", "* ```t``` is the time variable (for non-autonomous systems).\n" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "cell_style": "split" }, "outputs": [], "source": [ "from scipy.integrate import solve_ivp\n", "\n", "t = np.linspace(0.0,25.0,512)\n", "mu = 1.0\n", "y = [-0.1,-0.1]\n", "\n", "def oscillator(t,y):\n", " solution = [mu*(y[1] - ((y[0]**3.0)/3.0 - y[0])), -y[0]/mu]\n", " return solution\n" ] }, { "cell_type": "markdown", "metadata": { "cell_style": "split", "slideshow": { "slide_type": "slide" } }, "source": [ "### Step 2: integrate via ```solve_ivp```" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "cell_style": "split" }, "outputs": [ { "data": { "text/plain": [ " message: 'The solver successfully reached the end of the integration interval.'\n", " nfev: 386\n", " njev: 0\n", " nlu: 0\n", " sol: None\n", " status: 0\n", " success: True\n", " t: array([ 0. , 0.04892368, 0.09784736, 0.14677104, 0.19569472,\n", " 0.2446184 , 0.29354207, 0.34246575, 0.39138943, 0.44031311,\n", " 0.48923679, 0.53816047, 0.58708415, 0.63600783, 0.68493151,\n", " 0.73385519, 0.78277886, 0.83170254, 0.88062622, 0.9295499 ,\n", " 0.97847358, 1.02739726, 1.07632094, 1.12524462, 1.1741683 ,\n", " 1.22309198, 1.27201566, 1.32093933, 1.36986301, 1.41878669,\n", " 1.46771037, 1.51663405, 1.56555773, 1.61448141, 1.66340509,\n", " 1.71232877, 1.76125245, 1.81017613, 1.8590998 , 1.90802348,\n", " 1.95694716, 2.00587084, 2.05479452, 2.1037182 , 2.15264188,\n", " 2.20156556, 2.25048924, 2.29941292, 2.34833659, 2.39726027,\n", " 2.44618395, 2.49510763, 2.54403131, 2.59295499, 2.64187867,\n", " 2.69080235, 2.73972603, 2.78864971, 2.83757339, 2.88649706,\n", " 2.93542074, 2.98434442, 3.0332681 , 3.08219178, 3.13111546,\n", " 3.18003914, 3.22896282, 3.2778865 , 3.32681018, 3.37573386,\n", " 3.42465753, 3.47358121, 3.52250489, 3.57142857, 3.62035225,\n", " 3.66927593, 3.71819961, 3.76712329, 3.81604697, 3.86497065,\n", " 3.91389432, 3.962818 , 4.01174168, 4.06066536, 4.10958904,\n", " 4.15851272, 4.2074364 , 4.25636008, 4.30528376, 4.35420744,\n", " 4.40313112, 4.45205479, 4.50097847, 4.54990215, 4.59882583,\n", " 4.64774951, 4.69667319, 4.74559687, 4.79452055, 4.84344423,\n", " 4.89236791, 4.94129159, 4.99021526, 5.03913894, 5.08806262,\n", " 5.1369863 , 5.18590998, 5.23483366, 5.28375734, 5.33268102,\n", " 5.3816047 , 5.43052838, 5.47945205, 5.52837573, 5.57729941,\n", " 5.62622309, 5.67514677, 5.72407045, 5.77299413, 5.82191781,\n", " 5.87084149, 5.91976517, 5.96868885, 6.01761252, 6.0665362 ,\n", " 6.11545988, 6.16438356, 6.21330724, 6.26223092, 6.3111546 ,\n", " 6.36007828, 6.40900196, 6.45792564, 6.50684932, 6.55577299,\n", " 6.60469667, 6.65362035, 6.70254403, 6.75146771, 6.80039139,\n", " 6.84931507, 6.89823875, 6.94716243, 6.99608611, 7.04500978,\n", " 7.09393346, 7.14285714, 7.19178082, 7.2407045 , 7.28962818,\n", " 7.33855186, 7.38747554, 7.43639922, 7.4853229 , 7.53424658,\n", " 7.58317025, 7.63209393, 7.68101761, 7.72994129, 7.77886497,\n", " 7.82778865, 7.87671233, 7.92563601, 7.97455969, 8.02348337,\n", " 8.07240705, 8.12133072, 8.1702544 , 8.21917808, 8.26810176,\n", " 8.31702544, 8.36594912, 8.4148728 , 8.46379648, 8.51272016,\n", " 8.56164384, 8.61056751, 8.65949119, 8.70841487, 8.75733855,\n", " 8.80626223, 8.85518591, 8.90410959, 8.95303327, 9.00195695,\n", " 9.05088063, 9.09980431, 9.14872798, 9.19765166, 9.24657534,\n", " 9.29549902, 9.3444227 , 9.39334638, 9.44227006, 9.49119374,\n", " 9.54011742, 9.5890411 , 9.63796477, 9.68688845, 9.73581213,\n", " 9.78473581, 9.83365949, 9.88258317, 9.93150685, 9.98043053,\n", " 10.02935421, 10.07827789, 10.12720157, 10.17612524, 10.22504892,\n", " 10.2739726 , 10.32289628, 10.37181996, 10.42074364, 10.46966732,\n", " 10.518591 , 10.56751468, 10.61643836, 10.66536204, 10.71428571,\n", " 10.76320939, 10.81213307, 10.86105675, 10.90998043, 10.95890411,\n", " 11.00782779, 11.05675147, 11.10567515, 11.15459883, 11.2035225 ,\n", " 11.25244618, 11.30136986, 11.35029354, 11.39921722, 11.4481409 ,\n", " 11.49706458, 11.54598826, 11.59491194, 11.64383562, 11.6927593 ,\n", " 11.74168297, 11.79060665, 11.83953033, 11.88845401, 11.93737769,\n", " 11.98630137, 12.03522505, 12.08414873, 12.13307241, 12.18199609,\n", " 12.23091977, 12.27984344, 12.32876712, 12.3776908 , 12.42661448,\n", " 12.47553816, 12.52446184, 12.57338552, 12.6223092 , 12.67123288,\n", " 12.72015656, 12.76908023, 12.81800391, 12.86692759, 12.91585127,\n", " 12.96477495, 13.01369863, 13.06262231, 13.11154599, 13.16046967,\n", " 13.20939335, 13.25831703, 13.3072407 , 13.35616438, 13.40508806,\n", " 13.45401174, 13.50293542, 13.5518591 , 13.60078278, 13.64970646,\n", " 13.69863014, 13.74755382, 13.7964775 , 13.84540117, 13.89432485,\n", " 13.94324853, 13.99217221, 14.04109589, 14.09001957, 14.13894325,\n", " 14.18786693, 14.23679061, 14.28571429, 14.33463796, 14.38356164,\n", " 14.43248532, 14.481409 , 14.53033268, 14.57925636, 14.62818004,\n", " 14.67710372, 14.7260274 , 14.77495108, 14.82387476, 14.87279843,\n", " 14.92172211, 14.97064579, 15.01956947, 15.06849315, 15.11741683,\n", " 15.16634051, 15.21526419, 15.26418787, 15.31311155, 15.36203523,\n", " 15.4109589 , 15.45988258, 15.50880626, 15.55772994, 15.60665362,\n", " 15.6555773 , 15.70450098, 15.75342466, 15.80234834, 15.85127202,\n", " 15.90019569, 15.94911937, 15.99804305, 16.04696673, 16.09589041,\n", " 16.14481409, 16.19373777, 16.24266145, 16.29158513, 16.34050881,\n", " 16.38943249, 16.43835616, 16.48727984, 16.53620352, 16.5851272 ,\n", " 16.63405088, 16.68297456, 16.73189824, 16.78082192, 16.8297456 ,\n", " 16.87866928, 16.92759295, 16.97651663, 17.02544031, 17.07436399,\n", " 17.12328767, 17.17221135, 17.22113503, 17.27005871, 17.31898239,\n", " 17.36790607, 17.41682975, 17.46575342, 17.5146771 , 17.56360078,\n", " 17.61252446, 17.66144814, 17.71037182, 17.7592955 , 17.80821918,\n", " 17.85714286, 17.90606654, 17.95499022, 18.00391389, 18.05283757,\n", " 18.10176125, 18.15068493, 18.19960861, 18.24853229, 18.29745597,\n", " 18.34637965, 18.39530333, 18.44422701, 18.49315068, 18.54207436,\n", " 18.59099804, 18.63992172, 18.6888454 , 18.73776908, 18.78669276,\n", " 18.83561644, 18.88454012, 18.9334638 , 18.98238748, 19.03131115,\n", " 19.08023483, 19.12915851, 19.17808219, 19.22700587, 19.27592955,\n", " 19.32485323, 19.37377691, 19.42270059, 19.47162427, 19.52054795,\n", " 19.56947162, 19.6183953 , 19.66731898, 19.71624266, 19.76516634,\n", " 19.81409002, 19.8630137 , 19.91193738, 19.96086106, 20.00978474,\n", " 20.05870841, 20.10763209, 20.15655577, 20.20547945, 20.25440313,\n", " 20.30332681, 20.35225049, 20.40117417, 20.45009785, 20.49902153,\n", " 20.54794521, 20.59686888, 20.64579256, 20.69471624, 20.74363992,\n", " 20.7925636 , 20.84148728, 20.89041096, 20.93933464, 20.98825832,\n", " 21.037182 , 21.08610568, 21.13502935, 21.18395303, 21.23287671,\n", " 21.28180039, 21.33072407, 21.37964775, 21.42857143, 21.47749511,\n", " 21.52641879, 21.57534247, 21.62426614, 21.67318982, 21.7221135 ,\n", " 21.77103718, 21.81996086, 21.86888454, 21.91780822, 21.9667319 ,\n", " 22.01565558, 22.06457926, 22.11350294, 22.16242661, 22.21135029,\n", " 22.26027397, 22.30919765, 22.35812133, 22.40704501, 22.45596869,\n", " 22.50489237, 22.55381605, 22.60273973, 22.65166341, 22.70058708,\n", " 22.74951076, 22.79843444, 22.84735812, 22.8962818 , 22.94520548,\n", " 22.99412916, 23.04305284, 23.09197652, 23.1409002 , 23.18982387,\n", " 23.23874755, 23.28767123, 23.33659491, 23.38551859, 23.43444227,\n", " 23.48336595, 23.53228963, 23.58121331, 23.63013699, 23.67906067,\n", " 23.72798434, 23.77690802, 23.8258317 , 23.87475538, 23.92367906,\n", " 23.97260274, 24.02152642, 24.0704501 , 24.11937378, 24.16829746,\n", " 24.21722114, 24.26614481, 24.31506849, 24.36399217, 24.41291585,\n", " 24.46183953, 24.51076321, 24.55968689, 24.60861057, 24.65753425,\n", " 24.70645793, 24.7553816 , 24.80430528, 24.85322896, 24.90215264,\n", " 24.95107632, 25. ])\n", " t_events: None\n", " y: array([[-0.1 , -0.10988309, -0.11998616, ..., 1.55227716,\n", " 1.51474726, 1.47599023],\n", " [-0.1 , -0.0948668 , -0.08924467, ..., -1.06117849,\n", " -1.1362059 , -1.20936825]])\n", " y_events: None" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "RelOsc = solve_ivp(oscillator, [0,25], y0 = y, t_eval = t)\n", "\n", "RelOsc" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Step 3: plot and analyse the solution\n" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# The start of the phase plane\n", "\n", "plt.rcParams.update({'font.size': 22})\n", "plt.figure(figsize=(10, 6))\n", "\n", "plt.plot(RelOsc.y[0],RelOsc.y[1], label = r\"$x(t),y(t)$\")\n", "\n", "plt.xlabel(r\"$x$\")\n", "plt.ylabel(r\"$y$\")\n", "plt.legend(loc=\"upper left\")\n", "plt.grid()\n", "plt.show()\n", "\n", "# Plot as a function of time\n", "\n", "plt.rcParams.update({'font.size': 22})\n", "plt.figure(figsize=(12, 6))\n", "\n", "plt.plot(t,RelOsc.y[0], label = r\"$x(t)$\")\n", "plt.plot(t,RelOsc.y[1], label = r\"$y(t)$\")\n", "\n", "plt.xlabel(r\"$t$\")\n", "plt.ylabel(r\"$x,y$\")\n", "\n", "plt.grid()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Comparison of Forward and Backward Euler for decay equation" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Two timescales in relaxation oscillator\n", "\n", "As practice you can try to implement your own formulae for the following decay equation: $u(t) = u_0 \\exp(-\\lambda t)$, with $u_0 = 100.0$ and $\\lambda = 10.0$ for example. (This may bring back (happy?) memories of your MathSys interviews!)\n", "\n", "Try implementing:\n", "* the Forward Euler method\n", "* the implicit Euler method\n", "* any other improvements\n", "\n", "Here is a sample solution for guidance:\n", "\"array\" " ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "cell_style": "split" }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Try changing mu (and run over longer timescales)\n", "t = np.linspace(0.0,250.0,2048)\n", "mu = 10.0\n", "\n", "RelOsc = solve_ivp(oscillator, [0,250], y0 = y, t_eval = t)\n", "\n", "plt.rcParams.update({'font.size': 22})\n", "plt.figure(figsize=(10, 6))\n", "\n", "plt.plot(RelOsc.y[0],RelOsc.y[1], label = r\"$x(t),y(t)$\")\n", "\n", "plt.xlabel(r\"$x$\")\n", "plt.ylabel(r\"$y$\")\n", "plt.legend(loc=\"upper left\")\n", "plt.grid()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "cell_style": "split" }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Plot with new parameters as a function of time\n", "\n", "plt.rcParams.update({'font.size': 22})\n", "plt.figure(figsize=(12, 6))\n", "\n", "plt.plot(t,RelOsc.y[0], label = r\"$x(t)$\")\n", "plt.plot(t,RelOsc.y[1], label = r\"$y(t)$\")\n", "\n", "plt.xlabel(r\"$t$\")\n", "plt.ylabel(r\"$x,y$\")\n", "\n", "plt.grid()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "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": "3.8.5" } }, "nbformat": 4, "nbformat_minor": 2 }