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Created September 8, 2021 06:56
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In this notebook, we use the package [`bseries.py`](https://github.com/ketch/bseries) to derive modified equations for certain Runge-Kutta methods applied to first-order ODEs, and study how well the solution of the modified equations approximates the numerical solution."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"from BSeries import trees, bs\n",
"import matplotlib.pyplot as plt\n",
"from nodepy import rk, ivp\n",
"from IPython.display import display, Math\n",
"import sympy\n",
"from sympy import symbols, simplify, lambdify, dsolve, Eq, Function\n",
"from sympy import Derivative as D\n",
"from sympy.abc import t\n",
"cf = trees.canonical_forest\n",
"one = sympy.Rational(1)\n",
"from sympy import sin\n",
"from scipy.integrate import solve_ivp\n",
"h = sympy.Symbol('h')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Lotka-Volterra"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here we reproduce the example from p. 340 of the book *Geometric Numerical Integration* (Hairer, Lubich, & Wanner), using the explicit Euler method to solve the Lotka-Volterra model:\n",
"\n",
"$$\n",
" p'(t) = (2-q)p \\quad \\quad q'(t)=(p-1)q.\n",
"$$\n",
"\n",
"First we define the model:"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"p, q = symbols('p,q')\n",
"u = [p,q]\n",
"f = np.array([p*(2-q),q*(p-1)])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Next, we load the coefficients of the method and generate the modified equations as a B-series:"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\left[\\begin{matrix}\\frac{p \\left(h \\left(q \\left(p - 1\\right) - \\left(q - 2\\right)^{2}\\right) - 2 q + 4\\right)}{2} & \\frac{q \\left(h \\left(p \\left(q - 2\\right) - \\left(p - 1\\right)^{2}\\right) + 2 p - 2\\right)}{2}\\end{matrix}\\right]$"
],
"text/plain": [
"[p*(h*(q*(p - 1) - (q - 2)**2) - 2*q + 4)/2, q*(h*(p*(q - 2) - (p - 1)**2) + 2*p - 2)/2]"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"FE1 = rk.loadRKM('FE')\n",
"\n",
"A = FE1.A\n",
"b = FE1.b\n",
"\n",
"series = bs.modified_equation(u, f, A, b, order=2)\n",
"simplify(series)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The numerical solution of the LV model by the explicit Euler method is the exact solution to a system of *modified differential equations*; this system can be expressed as a power series in the step size $h$. Here we have derived the right had side of that system up to terms of order $h$. Notice that if we drop the $O(h)$ terms then we have again the original LV system."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can check that the $O(h)$ terms match what is given in HLW:"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle - p q + q^{2} - 3 q + 4$"
],
"text/plain": [
"-p*q + q**2 - 3*q + 4"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"-sympy.expand(simplify(series[0]+p*(q-2))*2/(h*p))"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle p^{2} - p q + 1$"
],
"text/plain": [
"p**2 - p*q + 1"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"-simplify(series[1]-q*(p-1))*2/(h*q)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Next, we'll solve the modified equations very accurately and compare the result with the numerical solution given by the explicit Euler method with step size $h=0.1$."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"dt = 0.1\n",
"T = 15.\n",
"IC = [1.5,2.25]\n",
"\n",
"fs = simplify(np.array([term.series(h,0,2).removeO() for term in series]))\n",
"f_ = lambdify([p,q,h],fs)\n",
"\n",
"def f_p_vec(t,u,h=dt):\n",
" return f_(*u,h)\n",
"\n",
"soln = solve_ivp(f_p_vec,[0,T],IC,t_eval=np.linspace(0,T,1000),rtol=1.e-12,atol=1.e-12,method='RK45')\n",
"\n",
"t1, y1 = soln.t, soln.y"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"f_ex = lambdify([p,q],f)\n",
"\n",
"def f_vec(t,u):\n",
" return f_ex(*u)\n",
"\n",
"\n",
"myivp = ivp.IVP(f=f_vec,u0=np.array(IC),T=T)\n",
"\n",
"t, y = FE1(myivp,dt=dt)\n",
"y = np.array(y)"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7fcdddc92730>"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 648x432 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(9,6))\n",
"plt.plot(y[:,1],y[:,0],'o')\n",
"plt.plot(y1[1,:],y1[0,:],'--k')\n",
"plt.xlim(0,9)\n",
"plt.ylim(0,5.5)\n",
"plt.legend(['Explicit Euler, dt=0.1','Modified flow to O(h)'],fontsize=15)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The exact solution of the LV model is periodic, but Euler's method generates a solution with growing amplitude. The modified equations accurately predict this.\n",
"\n",
"Now we go to the next order."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\left[\\begin{matrix}\\frac{p \\left(h^{2} q \\left(p - 1\\right) \\left(q - 2\\right) + 2 h^{2} \\left(p q \\left(q - 2\\right) - q \\left(p - 1\\right)^{2} + q \\left(p - 1\\right) \\left(q - 2\\right) - \\left(q - 2\\right)^{3}\\right) + 3 h \\left(q \\left(p - 1\\right) - \\left(q - 2\\right)^{2}\\right) - 6 q + 12\\right)}{6} & \\frac{q \\left(- h^{2} p \\left(p - 1\\right) \\left(q - 2\\right) + 2 h^{2} \\left(- p q \\left(p - 1\\right) - p \\left(p - 1\\right) \\left(q - 2\\right) + p \\left(q - 2\\right)^{2} + \\left(p - 1\\right)^{3}\\right) + 3 h \\left(p \\left(q - 2\\right) - \\left(p - 1\\right)^{2}\\right) + 6 p - 6\\right)}{6}\\end{matrix}\\right]$"
],
"text/plain": [
"[p*(h**2*q*(p - 1)*(q - 2) + 2*h**2*(p*q*(q - 2) - q*(p - 1)**2 + q*(p - 1)*(q - 2) - (q - 2)**3) + 3*h*(q*(p - 1) - (q - 2)**2) - 6*q + 12)/6, q*(-h**2*p*(p - 1)*(q - 2) + 2*h**2*(-p*q*(p - 1) - p*(p - 1)*(q - 2) + p*(q - 2)**2 + (p - 1)**3) + 3*h*(p*(q - 2) - (p - 1)**2) + 6*p - 6)/6]"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"series = bs.modified_equation(u, f, A, b, order=3)\n",
"simplify(series)"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [],
"source": [
"dt = 0.12\n",
"T = 14.5\n",
"IC = [1.,2.75]\n",
"\n",
"fs = simplify(np.array([term.series(h,0,2).removeO() for term in series]))\n",
"f_ = lambdify([p,q,h],fs)\n",
"def f_p_vec(t,u,h=dt):\n",
" return f_(*u,h)\n",
"soln = solve_ivp(f_p_vec,[0,T],IC,t_eval=np.linspace(0,T,1000),rtol=1.e-12,atol=1.e-12,method='RK45')\n",
"t1, y1 = soln.t, soln.y\n",
"\n",
"fs = simplify(np.array([term.series(h,0,3).removeO() for term in series]))\n",
"f_ = lambdify([p,q,h],fs)\n",
"def f_p_vec(t,u,h=dt):\n",
" return f_(*u,h)\n",
"soln = solve_ivp(f_p_vec,[0,T],IC,t_eval=np.linspace(0,T,1000),rtol=1.e-12,atol=1.e-12,method='RK45')\n",
"t2, y2 = soln.t, soln.y\n",
"\n",
"f_ex = lambdify([p,q],f)\n",
"\n",
"def f_vec(t,u):\n",
" return f_ex(*u)\n",
"\n",
"\n",
"myivp = ivp.IVP(f=f_vec,u0=np.array(IC),T=T)\n",
"\n",
"t, y = FE1(myivp,dt=dt)\n",
"y = np.array(y)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 648x432 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(9,6))\n",
"plt.plot(y[:,1],y[:,0],'o')\n",
"plt.plot(y1[1,:],y1[0,:],'--')\n",
"plt.plot(y2[1,:],y2[0,:],'--k')\n",
"plt.xlim(0,9)\n",
"plt.ylim(0,5.5)\n",
"plt.legend(['Explicit Euler, dt=0.12','Modified flow to $O(h)$','Modified flow to $O(h^2)$'],fontsize=15);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Using a larger step size, we see that the 1st-order modified equations are not fully accurate, but by including the $O(h^2)$ terms we get much better accuracy at late times.\n",
"\n",
"Let's keep going."
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\left[\\begin{matrix}\\frac{p \\left(3 h^{3} p^{3} q - 13 h^{3} p^{2} q^{2} + 9 h^{3} p^{2} q + 13 h^{3} p q^{3} - 34 h^{3} p q^{2} + 35 h^{3} p q - 3 h^{3} q^{4} + 18 h^{3} q^{3} - 53 h^{3} q^{2} + 77 h^{3} q - 48 h^{3} - 4 h^{2} p^{2} q + 10 h^{2} p q^{2} - 12 h^{2} p q - 4 h^{2} q^{3} + 18 h^{2} q^{2} - 40 h^{2} q + 32 h^{2} + 6 h p q - 6 h q^{2} + 18 h q - 24 h - 12 q + 24\\right)}{12} & \\frac{q \\left(- 3 h^{3} p^{4} + 13 h^{3} p^{3} q - 13 h^{3} p^{2} q^{2} + 10 h^{3} p^{2} q - 14 h^{3} p^{2} + 3 h^{3} p q^{3} - 9 h^{3} p q^{2} + 23 h^{3} p q - 8 h^{3} p - 3 h^{3} + 4 h^{2} p^{3} - 10 h^{2} p^{2} q + 4 h^{2} p q^{2} - 6 h^{2} p q + 16 h^{2} p - 4 h^{2} - 6 h p^{2} + 6 h p q - 6 h + 12 p - 12\\right)}{12}\\end{matrix}\\right]$"
],
"text/plain": [
"[p*(3*h**3*p**3*q - 13*h**3*p**2*q**2 + 9*h**3*p**2*q + 13*h**3*p*q**3 - 34*h**3*p*q**2 + 35*h**3*p*q - 3*h**3*q**4 + 18*h**3*q**3 - 53*h**3*q**2 + 77*h**3*q - 48*h**3 - 4*h**2*p**2*q + 10*h**2*p*q**2 - 12*h**2*p*q - 4*h**2*q**3 + 18*h**2*q**2 - 40*h**2*q + 32*h**2 + 6*h*p*q - 6*h*q**2 + 18*h*q - 24*h - 12*q + 24)/12, q*(-3*h**3*p**4 + 13*h**3*p**3*q - 13*h**3*p**2*q**2 + 10*h**3*p**2*q - 14*h**3*p**2 + 3*h**3*p*q**3 - 9*h**3*p*q**2 + 23*h**3*p*q - 8*h**3*p - 3*h**3 + 4*h**2*p**3 - 10*h**2*p**2*q + 4*h**2*p*q**2 - 6*h**2*p*q + 16*h**2*p - 4*h**2 - 6*h*p**2 + 6*h*p*q - 6*h + 12*p - 12)/12]"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"series = bs.modified_equation(u, f, A, b, order=4)\n",
"simplify(series)"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [],
"source": [
"dt = 0.2\n",
"T = 10.\n",
"IC = [1.,2.75]\n",
"\n",
"fs = simplify(np.array([term.series(h,0,2).removeO() for term in series]))\n",
"f_ = lambdify([p,q,h],fs)\n",
"def f_p_vec(t,u,h=dt):\n",
" return f_(*u,h)\n",
"soln = solve_ivp(f_p_vec,[0,T],IC,t_eval=np.linspace(0,T,1000),rtol=1.e-12,atol=1.e-12,method='RK45')\n",
"t1, y1 = soln.t, soln.y\n",
"\n",
"fs = simplify(np.array([term.series(h,0,3).removeO() for term in series]))\n",
"f_ = lambdify([p,q,h],fs)\n",
"def f_p_vec(t,u,h=dt):\n",
" return f_(*u,h)\n",
"soln = solve_ivp(f_p_vec,[0,T],IC,t_eval=np.linspace(0,T,1000),rtol=1.e-12,atol=1.e-12,method='RK45')\n",
"t2, y2 = soln.t, soln.y\n",
"\n",
"fs = simplify(np.array([term.series(h,0,4).removeO() for term in series]))\n",
"f_ = lambdify([p,q,h],fs)\n",
"def f_p_vec(t,u,h=dt):\n",
" return f_(*u,h)\n",
"soln = solve_ivp(f_p_vec,[0,T],IC,t_eval=np.linspace(0,T,1000),rtol=1.e-12,atol=1.e-12,method='RK45')\n",
"t3, y3 = soln.t, soln.y\n",
"\n",
"\n",
"\n",
"f_ex = lambdify([p,q],f)\n",
"\n",
"def f_vec(t,u):\n",
" return f_ex(*u)\n",
"\n",
"\n",
"myivp = ivp.IVP(f=f_vec,u0=np.array(IC),T=T)\n",
"\n",
"t, y = FE1(myivp,dt=dt)\n",
"y = np.array(y)"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7fcddeb08370>"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 648x432 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(9,6))\n",
"plt.plot(y[:,1],y[:,0],'o')\n",
"plt.plot(y1[1,:],y1[0,:],'--')\n",
"plt.plot(y2[1,:],y2[0,:],'--')\n",
"plt.plot(y3[1,:],y3[0,:],'--k')\n",
"plt.xlim(0,15)\n",
"plt.ylim(-0.5,6.5)\n",
"plt.legend(['Explicit Euler, dt='+str(dt),'Modified flow to $O(h)$','Modified flow to $O(h^2)$','Modified flow to $O(h^3)$'],fontsize=15)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Again, with a larger step size we see that additional terms are needed to obtain good accuracy at later times."
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\left[\\begin{matrix}\\frac{p \\left(- 60 h^{6} p^{6} q + 669 h^{6} p^{5} q^{2} - 180 h^{6} p^{5} q - 2216 h^{6} p^{4} q^{3} + 1989 h^{6} p^{4} q^{2} - 760 h^{6} p^{4} q + 3196 h^{6} p^{3} q^{4} - 7136 h^{6} p^{3} q^{3} + 7296 h^{6} p^{3} q^{2} - 1960 h^{6} p^{3} q - 2216 h^{6} p^{2} q^{5} + 9809 h^{6} p^{2} q^{4} - 19671 h^{6} p^{2} q^{3} + 17314 h^{6} p^{2} q^{2} - 5740 h^{6} p^{2} q + 669 h^{6} p q^{6} - 4890 h^{6} p q^{5} + 16587 h^{6} p q^{4} - 30778 h^{6} p q^{3} + 31119 h^{6} p q^{2} - 13244 h^{6} p q - 60 h^{6} q^{7} + 630 h^{6} q^{6} - 3220 h^{6} q^{5} + 10150 h^{6} q^{4} - 20923 h^{6} q^{3} + 27797 h^{6} q^{2} - 21816 h^{6} q + 7680 h^{6} + 70 h^{5} p^{5} q - 609 h^{5} p^{4} q^{2} + 210 h^{5} p^{4} q + 1519 h^{5} p^{3} q^{3} - 1855 h^{5} p^{3} q^{2} + 896 h^{5} p^{3} q - 1519 h^{5} p^{2} q^{4} + 4550 h^{5} p^{2} q^{3} - 6013 h^{5} p^{2} q^{2} + 2352 h^{5} p^{2} q + 609 h^{5} p q^{5} - 3472 h^{5} p q^{4} + 9100 h^{5} p q^{3} - 11543 h^{5} p q^{2} + 6146 h^{5} p q - 70 h^{5} q^{6} + 630 h^{5} q^{5} - 2765 h^{5} q^{4} + 7245 h^{5} q^{3} - 11732 h^{5} q^{2} + 10878 h^{5} q - 4480 h^{5} - 84 h^{4} p^{4} q + 539 h^{4} p^{3} q^{2} - 252 h^{4} p^{3} q - 924 h^{4} p^{2} q^{3} + 1596 h^{4} p^{2} q^{2} - 1050 h^{4} p^{2} q + 539 h^{4} p q^{4} - 2226 h^{4} p q^{3} + 4109 h^{4} p q^{2} - 2660 h^{4} p q - 84 h^{4} q^{5} + 630 h^{4} q^{4} - 2310 h^{4} q^{3} + 4760 h^{4} q^{2} - 5474 h^{4} q + 2688 h^{4} + 105 h^{3} p^{3} q - 455 h^{3} p^{2} q^{2} + 315 h^{3} p^{2} q + 455 h^{3} p q^{3} - 1190 h^{3} p q^{2} + 1225 h^{3} p q - 105 h^{3} q^{4} + 630 h^{3} q^{3} - 1855 h^{3} q^{2} + 2695 h^{3} q - 1680 h^{3} - 140 h^{2} p^{2} q + 350 h^{2} p q^{2} - 420 h^{2} p q - 140 h^{2} q^{3} + 630 h^{2} q^{2} - 1400 h^{2} q + 1120 h^{2} + 210 h p q - 210 h q^{2} + 630 h q - 840 h - 420 q + 840\\right)}{420} & \\frac{q \\left(60 h^{6} p^{7} - 669 h^{6} p^{6} q + 2216 h^{6} p^{5} q^{2} - 255 h^{6} p^{5} q + 280 h^{6} p^{5} - 3196 h^{6} p^{4} q^{3} + 2588 h^{6} p^{4} q^{2} - 2952 h^{6} p^{4} q - 140 h^{6} p^{4} + 2216 h^{6} p^{3} q^{4} - 5261 h^{6} p^{3} q^{3} + 8712 h^{6} p^{3} q^{2} - 3052 h^{6} p^{3} q + 868 h^{6} p^{3} - 669 h^{6} p^{2} q^{5} + 3156 h^{6} p^{2} q^{4} - 8355 h^{6} p^{2} q^{3} + 10126 h^{6} p^{2} q^{2} - 7203 h^{6} p^{2} q + 728 h^{6} p^{2} + 60 h^{6} p q^{6} - 450 h^{6} p q^{5} + 1840 h^{6} p q^{4} - 4450 h^{6} p q^{3} + 6970 h^{6} p q^{2} - 5957 h^{6} p q + 2664 h^{6} p - 60 h^{6} - 70 h^{5} p^{6} + 609 h^{5} p^{5} q - 1519 h^{5} p^{4} q^{2} + 364 h^{5} p^{4} q - 350 h^{5} p^{4} + 1519 h^{5} p^{3} q^{3} - 1904 h^{5} p^{3} q^{2} + 2464 h^{5} p^{3} q - 609 h^{5} p^{2} q^{4} + 1981 h^{5} p^{2} q^{3} - 4165 h^{5} p^{2} q^{2} + 2576 h^{5} p^{2} q - 1022 h^{5} p^{2} + 70 h^{5} p q^{5} - 420 h^{5} p q^{4} + 1463 h^{5} p q^{3} - 2688 h^{5} p q^{2} + 3143 h^{5} p q - 1176 h^{5} p - 70 h^{5} + 84 h^{4} p^{5} - 539 h^{4} p^{4} q + 924 h^{4} p^{3} q^{2} - 399 h^{4} p^{3} q + 420 h^{4} p^{3} - 539 h^{4} p^{2} q^{3} + 1029 h^{4} p^{2} q^{2} - 1715 h^{4} p^{2} q + 140 h^{4} p^{2} + 84 h^{4} p q^{4} - 378 h^{4} p q^{3} + 1113 h^{4} p q^{2} - 1295 h^{4} p q + 1064 h^{4} p - 84 h^{4} - 105 h^{3} p^{4} + 455 h^{3} p^{3} q - 455 h^{3} p^{2} q^{2} + 350 h^{3} p^{2} q - 490 h^{3} p^{2} + 105 h^{3} p q^{3} - 315 h^{3} p q^{2} + 805 h^{3} p q - 280 h^{3} p - 105 h^{3} + 140 h^{2} p^{3} - 350 h^{2} p^{2} q + 140 h^{2} p q^{2} - 210 h^{2} p q + 560 h^{2} p - 140 h^{2} - 210 h p^{2} + 210 h p q - 210 h + 420 p - 420\\right)}{420}\\end{matrix}\\right]$"
],
"text/plain": [
"[p*(-60*h**6*p**6*q + 669*h**6*p**5*q**2 - 180*h**6*p**5*q - 2216*h**6*p**4*q**3 + 1989*h**6*p**4*q**2 - 760*h**6*p**4*q + 3196*h**6*p**3*q**4 - 7136*h**6*p**3*q**3 + 7296*h**6*p**3*q**2 - 1960*h**6*p**3*q - 2216*h**6*p**2*q**5 + 9809*h**6*p**2*q**4 - 19671*h**6*p**2*q**3 + 17314*h**6*p**2*q**2 - 5740*h**6*p**2*q + 669*h**6*p*q**6 - 4890*h**6*p*q**5 + 16587*h**6*p*q**4 - 30778*h**6*p*q**3 + 31119*h**6*p*q**2 - 13244*h**6*p*q - 60*h**6*q**7 + 630*h**6*q**6 - 3220*h**6*q**5 + 10150*h**6*q**4 - 20923*h**6*q**3 + 27797*h**6*q**2 - 21816*h**6*q + 7680*h**6 + 70*h**5*p**5*q - 609*h**5*p**4*q**2 + 210*h**5*p**4*q + 1519*h**5*p**3*q**3 - 1855*h**5*p**3*q**2 + 896*h**5*p**3*q - 1519*h**5*p**2*q**4 + 4550*h**5*p**2*q**3 - 6013*h**5*p**2*q**2 + 2352*h**5*p**2*q + 609*h**5*p*q**5 - 3472*h**5*p*q**4 + 9100*h**5*p*q**3 - 11543*h**5*p*q**2 + 6146*h**5*p*q - 70*h**5*q**6 + 630*h**5*q**5 - 2765*h**5*q**4 + 7245*h**5*q**3 - 11732*h**5*q**2 + 10878*h**5*q - 4480*h**5 - 84*h**4*p**4*q + 539*h**4*p**3*q**2 - 252*h**4*p**3*q - 924*h**4*p**2*q**3 + 1596*h**4*p**2*q**2 - 1050*h**4*p**2*q + 539*h**4*p*q**4 - 2226*h**4*p*q**3 + 4109*h**4*p*q**2 - 2660*h**4*p*q - 84*h**4*q**5 + 630*h**4*q**4 - 2310*h**4*q**3 + 4760*h**4*q**2 - 5474*h**4*q + 2688*h**4 + 105*h**3*p**3*q - 455*h**3*p**2*q**2 + 315*h**3*p**2*q + 455*h**3*p*q**3 - 1190*h**3*p*q**2 + 1225*h**3*p*q - 105*h**3*q**4 + 630*h**3*q**3 - 1855*h**3*q**2 + 2695*h**3*q - 1680*h**3 - 140*h**2*p**2*q + 350*h**2*p*q**2 - 420*h**2*p*q - 140*h**2*q**3 + 630*h**2*q**2 - 1400*h**2*q + 1120*h**2 + 210*h*p*q - 210*h*q**2 + 630*h*q - 840*h - 420*q + 840)/420, q*(60*h**6*p**7 - 669*h**6*p**6*q + 2216*h**6*p**5*q**2 - 255*h**6*p**5*q + 280*h**6*p**5 - 3196*h**6*p**4*q**3 + 2588*h**6*p**4*q**2 - 2952*h**6*p**4*q - 140*h**6*p**4 + 2216*h**6*p**3*q**4 - 5261*h**6*p**3*q**3 + 8712*h**6*p**3*q**2 - 3052*h**6*p**3*q + 868*h**6*p**3 - 669*h**6*p**2*q**5 + 3156*h**6*p**2*q**4 - 8355*h**6*p**2*q**3 + 10126*h**6*p**2*q**2 - 7203*h**6*p**2*q + 728*h**6*p**2 + 60*h**6*p*q**6 - 450*h**6*p*q**5 + 1840*h**6*p*q**4 - 4450*h**6*p*q**3 + 6970*h**6*p*q**2 - 5957*h**6*p*q + 2664*h**6*p - 60*h**6 - 70*h**5*p**6 + 609*h**5*p**5*q - 1519*h**5*p**4*q**2 + 364*h**5*p**4*q - 350*h**5*p**4 + 1519*h**5*p**3*q**3 - 1904*h**5*p**3*q**2 + 2464*h**5*p**3*q - 609*h**5*p**2*q**4 + 1981*h**5*p**2*q**3 - 4165*h**5*p**2*q**2 + 2576*h**5*p**2*q - 1022*h**5*p**2 + 70*h**5*p*q**5 - 420*h**5*p*q**4 + 1463*h**5*p*q**3 - 2688*h**5*p*q**2 + 3143*h**5*p*q - 1176*h**5*p - 70*h**5 + 84*h**4*p**5 - 539*h**4*p**4*q + 924*h**4*p**3*q**2 - 399*h**4*p**3*q + 420*h**4*p**3 - 539*h**4*p**2*q**3 + 1029*h**4*p**2*q**2 - 1715*h**4*p**2*q + 140*h**4*p**2 + 84*h**4*p*q**4 - 378*h**4*p*q**3 + 1113*h**4*p*q**2 - 1295*h**4*p*q + 1064*h**4*p - 84*h**4 - 105*h**3*p**4 + 455*h**3*p**3*q - 455*h**3*p**2*q**2 + 350*h**3*p**2*q - 490*h**3*p**2 + 105*h**3*p*q**3 - 315*h**3*p*q**2 + 805*h**3*p*q - 280*h**3*p - 105*h**3 + 140*h**2*p**3 - 350*h**2*p**2*q + 140*h**2*p*q**2 - 210*h**2*p*q + 560*h**2*p - 140*h**2 - 210*h*p**2 + 210*h*p*q - 210*h + 420*p - 420)/420]"
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"series = bs.modified_equation(u, f, A, b, order=7)\n",
"simplify(series)"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [],
"source": [
"dt = 0.1\n",
"T = 66.4\n",
"IC = [1.,2.01]\n",
"N = 3000\n",
"fs = simplify(np.array([term.series(h,0,2).removeO() for term in series]))\n",
"f_ = lambdify([p,q,h],fs)\n",
"def f_p_vec(t,u,h=dt):\n",
" return f_(*u,h)\n",
"soln = solve_ivp(f_p_vec,[0,T],IC,t_eval=np.linspace(0,T,N),rtol=1.e-12,atol=1.e-12,method='RK45')\n",
"t1, y1 = soln.t, soln.y\n",
"\n",
"fs = simplify(np.array([term.series(h,0,3).removeO() for term in series]))\n",
"f_ = lambdify([p,q,h],fs)\n",
"def f_p_vec(t,u,h=dt):\n",
" return f_(*u,h)\n",
"soln = solve_ivp(f_p_vec,[0,T],IC,t_eval=np.linspace(0,T,N),rtol=1.e-12,atol=1.e-12,method='RK45')\n",
"t2, y2 = soln.t, soln.y\n",
"\n",
"fs = simplify(np.array([term.series(h,0,4).removeO() for term in series]))\n",
"f_ = lambdify([p,q,h],fs)\n",
"def f_p_vec(t,u,h=dt):\n",
" return f_(*u,h)\n",
"soln = solve_ivp(f_p_vec,[0,T],IC,t_eval=np.linspace(0,T,N),rtol=1.e-12,atol=1.e-12,method='RK45')\n",
"t3, y3 = soln.t, soln.y\n",
"\n",
"fs = simplify(np.array([term.series(h,0,7).removeO() for term in series]))\n",
"f_ = lambdify([p,q,h],fs)\n",
"def f_p_vec(t,u,h=dt):\n",
" return f_(*u,h)\n",
"soln = solve_ivp(f_p_vec,[0,T],IC,t_eval=np.linspace(0,T,N),rtol=1.e-12,atol=1.e-12,method='RK45')\n",
"t5, y5 = soln.t, soln.y\n",
"\n",
"\n",
"f_ex = lambdify([p,q],f)\n",
"\n",
"def f_vec(t,u):\n",
" return f_ex(*u)\n",
"\n",
"\n",
"myivp = ivp.IVP(f=f_vec,u0=np.array(IC),T=T)\n",
"\n",
"t, y = FE1(myivp,dt=dt)\n",
"y = np.array(y)"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 648x432 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(9,6))\n",
"plt.plot(y[:,1],y[:,0],'o')\n",
"plt.plot(y1[1,:],y1[0,:],'--')\n",
"plt.plot(y2[1,:],y2[0,:],'--')\n",
"plt.plot(y3[1,:],y3[0,:],'--')\n",
"plt.plot(y5[1,:],y5[0,:],'--k')\n",
"plt.xlim(-0.5,18)\n",
"plt.ylim(-0.5,11.5)\n",
"plt.legend(['Explicit Euler, dt='+str(dt),'Modified flow to $O(h)$','Modified flow to $O(h^2)$',\n",
" 'Modified flow to $O(h^3)$','Modified flow to $O(h^6)$'],fontsize=15);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here we have gone all the way up to the $O(h)^6$ terms and we continue to get improved accuracy for long times."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Pendulum"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Next we consider another simple first-order system of two equations that models a rigid frictionless pendulum (see e.g. p. 4 of HLW)."
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\left[\\begin{matrix}- \\sin{\\left(q \\right)} & p\\end{matrix}\\right]$"
],
"text/plain": [
"[-sin(q), p]"
]
},
"execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"f = np.array([-sin(u[1]),u[0]])\n",
"IC = [1.,0.]\n",
"simplify(f)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This time we'll consider a more accurate numerical method: a 3-stage, 3rd-order Runge-Kutta method."
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\left[\\begin{matrix}- \\frac{h^{5} p^{3} \\cos^{2}{\\left(q \\right)}}{96} - \\frac{5 h^{5} p \\cos^{3}{\\left(q \\right)}}{288} + \\frac{h^{5} p \\cos{\\left(q \\right)}}{32} - \\frac{h^{4} p^{4} \\sin{\\left(q \\right)}}{2880} + \\frac{h^{4} p^{2} \\sin{\\left(q \\right)} \\cos{\\left(q \\right)}}{120} + \\frac{h^{4} \\sin^{3}{\\left(q \\right)}}{20} - \\frac{h^{4} \\sin{\\left(q \\right)}}{30} - \\frac{h^{3} p \\cos^{2}{\\left(q \\right)}}{12} + \\frac{h^{3} p}{24} - \\sin{\\left(q \\right)} & \\frac{h^{5} p^{4} \\sin{\\left(q \\right)}}{1152} + \\frac{5 h^{5} p^{2} \\sin{\\left(2 q \\right)}}{576} + \\frac{h^{5} \\sin{\\left(q \\right)}}{288} + \\frac{h^{5} \\sin{\\left(3 q \\right)}}{288} - \\frac{h^{4} p^{3} \\cos{\\left(q \\right)}}{720} + \\frac{h^{4} p \\cos{\\left(2 q \\right)}}{240} + \\frac{7 h^{4} p}{240} + \\frac{h^{3} p^{2} \\sin{\\left(q \\right)}}{24} - \\frac{h^{3} \\sin{\\left(2 q \\right)}}{48} + p\\end{matrix}\\right]$"
],
"text/plain": [
"[-h**5*p**3*cos(q)**2/96 - 5*h**5*p*cos(q)**3/288 + h**5*p*cos(q)/32 - h**4*p**4*sin(q)/2880 + h**4*p**2*sin(q)*cos(q)/120 + h**4*sin(q)**3/20 - h**4*sin(q)/30 - h**3*p*cos(q)**2/12 + h**3*p/24 - sin(q), h**5*p**4*sin(q)/1152 + 5*h**5*p**2*sin(2*q)/576 + h**5*sin(q)/288 + h**5*sin(3*q)/288 - h**4*p**3*cos(q)/720 + h**4*p*cos(2*q)/240 + 7*h**4*p/240 + h**3*p**2*sin(q)/24 - h**3*sin(2*q)/48 + p]"
]
},
"execution_count": 19,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"rk3 = rk.loadRKM('SSP33')\n",
"A = rk3.A\n",
"b = rk3.b\n",
"\n",
"series = bs.modified_equation(u, f, A, b, order=6)\n",
"simplify(series)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Notice that the modified equations (which we have derived up to order $h^5$) include no correction terms of order $h$ or $h^2$. This is true because the method chosen is 3rd-order accurate.\n",
"\n",
"Again, we compare a highly-accurate solution of the modified equations with the approximate solution of the original problem obtained using the Runge-Kutta method."
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [],
"source": [
"dt = 1.05\n",
"T = 20\n",
"N=1000"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [],
"source": [
"def solve_truncated_modified_equations(order,dt):\n",
" f = simplify(np.array([term.series(h,0,order+1).removeO() for term in series]))\n",
" f_ = lambdify([p,q,h],f)\n",
" \n",
" def f_p_vec(t,u,h=dt):\n",
" return f_(*u,h)\n",
"\n",
" soln = solve_ivp(f_p_vec,[0,T],IC,t_eval=np.linspace(0,T,N),rtol=1.e-12,atol=1.e-12,method='RK45')\n",
"\n",
" return soln.t, soln.y\n",
"\n",
"tt = []\n",
"yy = []\n",
"for order in range(7):\n",
" t, y = solve_truncated_modified_equations(order,dt=dt)\n",
" tt.append(t)\n",
" yy.append(y)"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {},
"outputs": [],
"source": [
"f_ex = lambdify([p,q],f)\n",
"f_ex(0.,1.)\n",
"\n",
"def f_vec(t,u):\n",
" return f_ex(*u)\n",
"\n",
"\n",
"myivp = ivp.IVP(f=f_vec,u0=np.array(IC),T=T)\n",
"\n",
"t_rk3, y = rk3(myivp,dt=dt)\n",
"y = np.array(y)\n",
"y_rk3 = y[:,0]"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7fcdded8c7f0>"
]
},
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 1152x864 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(16,12))\n",
"\n",
"plt.plot(t_rk3,y_rk3,'o')\n",
"for i in range(2,6):\n",
" plt.plot(tt[i],yy[i][0,:],'--')\n",
"\n",
"plt.legend(['RK3']+['$O(h^'+str(p)+')$' for p in range(2,6)],fontsize=20)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can see that each successive correction gives a solution that is accurate to later times than the one previous. Notice that in this case, although the exact solution is periodic, the numerical solution is gradually damped, and this behavior is captured by the more accurate versions of the modified equations."
]
}
],
"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": "3.9.5"
},
"toc": {
"base_numbering": 1,
"nav_menu": {},
"number_sections": true,
"sideBar": true,
"skip_h1_title": false,
"title_cell": "Table of Contents",
"title_sidebar": "Contents",
"toc_cell": false,
"toc_position": {},
"toc_section_display": true,
"toc_window_display": false
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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