{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## Druhy chyb\n", "* Fyzikální aproximace - Newton/OTR...\n", "* Chyba vstupních parametrů - poč. podm., fyzikální konstanty...\n", "* Chyba metody - v důsledku diskretizace. Tím se budeme hlavně zabývat\n", "* Zaokrouhlovací chyba - v důsledku konečné přesnosti počítače\n", "\n", "# Numerické derivování\n", "\n", "Je základem numerických metod ve fyzice (ODR, PDR...)\n", "\n", "Jak vyhodnocováním $f(x)$ v různých bodech zjistit $f'(x)$? Vyjdeme z definice\n", "$$\n", "f'(x) = \\lim_{h\\to 0}\\frac{f(x+h)-f(x)}{h}\n", "$$\n", "\n", "Diskretizace, otázka přesnosti (chyba metody a zaokrouhlovací chyba), dopředné diference, centrální diference\n", "\n", "Asymptotické chování chyby a její eliminace - Richardsonova extrapolace\n", "\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "ExecuteTime": { "end_time": "2023-02-20T10:47:06.701093Z", "start_time": "2023-02-20T10:47:06.033338Z" }, "execution": { "iopub.execute_input": "2024-06-14T15:01:39.848344Z", "iopub.status.busy": "2024-06-14T15:01:39.847993Z", "iopub.status.idle": "2024-06-14T15:01:40.110876Z", "shell.execute_reply": "2024-06-14T15:01:40.110470Z", "shell.execute_reply.started": "2024-06-14T15:01:39.848300Z" } }, "outputs": [], "source": [ "%matplotlib inline\n", "%config InlineBackend.close_figures=False\n", "import pylab as P\n", "import numpy as N" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "ExecuteTime": { "end_time": "2023-02-20T10:47:07.838718Z", "start_time": "2023-02-20T10:47:07.833723Z" }, "execution": { "iopub.execute_input": "2024-06-14T15:01:40.111608Z", "iopub.status.busy": "2024-06-14T15:01:40.111450Z", "iopub.status.idle": "2024-06-14T15:01:40.113523Z", "shell.execute_reply": "2024-06-14T15:01:40.113267Z", "shell.execute_reply.started": "2024-06-14T15:01:40.111599Z" } }, "outputs": [], "source": [ "# definujeme funkci pro výpočet dopředných diferencí:\n", "def diff_FD(f, x, dx): return (f(x+dx) - f(x))/dx" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "ExecuteTime": { "end_time": "2023-02-20T10:47:26.295320Z", "start_time": "2023-02-20T10:47:26.292270Z" }, "execution": { "iopub.execute_input": "2024-06-14T15:01:40.113977Z", "iopub.status.busy": "2024-06-14T15:01:40.113841Z", "iopub.status.idle": "2024-06-14T15:01:40.115673Z", "shell.execute_reply": "2024-06-14T15:01:40.115410Z", "shell.execute_reply.started": "2024-06-14T15:01:40.113970Z" } }, "outputs": [], "source": [ "# asymptotická chyba dopředných diferencí určená Taylorovým rozvojem:\n", "def diff_FD_err(f, d2f, d3f, x, dx): return 0.5*d2f(x)*dx" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "ExecuteTime": { "end_time": "2023-02-20T10:47:36.187902Z", "start_time": "2023-02-20T10:47:36.184235Z" }, "execution": { "iopub.execute_input": "2024-06-14T15:01:40.116282Z", "iopub.status.busy": "2024-06-14T15:01:40.116077Z", "iopub.status.idle": "2024-06-14T15:01:40.117756Z", "shell.execute_reply": "2024-06-14T15:01:40.117583Z", "shell.execute_reply.started": "2024-06-14T15:01:40.116274Z" } }, "outputs": [], "source": [ "# použijeme sin(x) pro testování\n", "def f(x): return N.sin(x)\n", "def dfdx(x): return N.cos(x)\n", "def dfdx2(x): return -N.sin(x)\n", "def dfdx3(x): return -N.cos(x)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "ExecuteTime": { "end_time": "2023-02-20T10:47:38.616776Z", "start_time": "2023-02-20T10:47:38.612217Z" }, "execution": { "iopub.execute_input": "2024-06-14T15:01:40.118441Z", "iopub.status.busy": "2024-06-14T15:01:40.118324Z", "iopub.status.idle": "2024-06-14T15:01:40.119801Z", "shell.execute_reply": "2024-06-14T15:01:40.119637Z", "shell.execute_reply.started": "2024-06-14T15:01:40.118433Z" } }, "outputs": [], "source": [ "# vypočteme derivaci pro x0=1.0 pro následující hodnoty dx\n", "x0 = 1.0\n", "dx = N.logspace(-17, 1, 500)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "ExecuteTime": { "end_time": "2023-02-20T10:47:42.157880Z", "start_time": "2023-02-20T10:47:42.154890Z" }, "execution": { "iopub.execute_input": "2024-06-14T15:01:40.120217Z", "iopub.status.busy": "2024-06-14T15:01:40.120057Z", "iopub.status.idle": "2024-06-14T15:01:40.121665Z", "shell.execute_reply": "2024-06-14T15:01:40.121493Z", "shell.execute_reply.started": "2024-06-14T15:01:40.120210Z" } }, "outputs": [], "source": [ "def format_plot(show=True):\n", " from matplotlib.ticker import LogLocator\n", " P.gca().xaxis.set_major_locator(LogLocator(base=100., numticks=20))\n", " if show:\n", " P.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Chyba dopředných diferencí" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "ExecuteTime": { "end_time": "2023-02-20T10:47:48.241684Z", "start_time": "2023-02-20T10:47:47.693413Z" }, "execution": { "iopub.execute_input": "2024-06-14T15:01:40.122002Z", "iopub.status.busy": "2024-06-14T15:01:40.121927Z", "iopub.status.idle": "2024-06-14T15:01:40.292602Z", "shell.execute_reply": "2024-06-14T15:01:40.291944Z", "shell.execute_reply.started": "2024-06-14T15:01:40.121995Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "P.figure(figsize=(6,4))\n", "\n", "rel_err = N.abs((diff_FD(f, x0, dx) - dfdx(x0))/dfdx(x0))\n", "P.loglog(dx, rel_err)\n", " \n", "# nastavení vykreslování\n", "%config InlineBackend.close_figures=False\n", "P.ylim([1e-13, 1e1])\n", "format_plot(False)\n", "P.xlabel(\"step size\")\n", "P.ylabel(\"rel. error\")\n", "P.grid(which=\"both\")\n", "\n" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "ExecuteTime": { "end_time": "2023-02-20T10:49:15.298630Z", "start_time": "2023-02-20T10:49:14.878989Z" }, "execution": { "iopub.execute_input": "2024-06-14T15:01:40.293241Z", "iopub.status.busy": "2024-06-14T15:01:40.293124Z", "iopub.status.idle": "2024-06-14T15:01:40.443061Z", "shell.execute_reply": "2024-06-14T15:01:40.442778Z", "shell.execute_reply.started": "2024-06-14T15:01:40.293234Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# porovnáme s asymptotickou hodnotou chyby\n", "err = N.abs(diff_FD_err(f, dfdx2, dfdx3, x0, dx)/dfdx(x0))\n", "P.loglog(dx, err,\":k\")\n", "\n", "format_plot()" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "ExecuteTime": { "end_time": "2023-02-20T10:49:49.108024Z", "start_time": "2023-02-20T10:49:49.104555Z" }, "execution": { "iopub.execute_input": "2024-06-14T15:01:40.443487Z", "iopub.status.busy": "2024-06-14T15:01:40.443405Z", "iopub.status.idle": "2024-06-14T15:01:40.445326Z", "shell.execute_reply": "2024-06-14T15:01:40.445147Z", "shell.execute_reply.started": "2024-06-14T15:01:40.443480Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "sys.float_info(max=1.7976931348623157e+308, max_exp=1024, max_10_exp=308, min=2.2250738585072014e-308, min_exp=-1021, min_10_exp=-307, dig=15, mant_dig=53, epsilon=2.220446049250313e-16, radix=2, rounds=1)\n" ] } ], "source": [ "import sys\n", "print(sys.float_info)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "ExecuteTime": { "end_time": "2023-02-20T10:50:23.653564Z", "start_time": "2023-02-20T10:50:23.370796Z" }, "execution": { "iopub.execute_input": "2024-06-14T15:01:40.445691Z", "iopub.status.busy": "2024-06-14T15:01:40.445615Z", "iopub.status.idle": "2024-06-14T15:01:40.582513Z", "shell.execute_reply": "2024-06-14T15:01:40.582233Z", "shell.execute_reply.started": "2024-06-14T15:01:40.445685Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "P.loglog(dx, f(x0)*sys.float_info.epsilon/dx,\"--k\")\n", "\n", "format_plot()" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "ExecuteTime": { "end_time": "2023-02-20T10:58:33.845619Z", "start_time": "2023-02-20T10:58:33.842740Z" }, "execution": { "iopub.execute_input": "2024-06-14T15:01:40.582952Z", "iopub.status.busy": "2024-06-14T15:01:40.582866Z", "iopub.status.idle": "2024-06-14T15:01:40.584746Z", "shell.execute_reply": "2024-06-14T15:01:40.584559Z", "shell.execute_reply.started": "2024-06-14T15:01:40.582945Z" } }, "outputs": [], "source": [ "# definujeme funkce pro výpočet centrovaných diferencí:\n", "def diff_CD(f, x, dx): return (f(x+dx) - f(x-dx))/(2*dx)\n", "\n", "# ...a asymptotické chování chyby centrovaných diferencí:\n", "def diff_CD_err(f, d2f, d3f, x, dx): return 1/6.*d3f(x)*dx**2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Chyba centrálních diferencí" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "ExecuteTime": { "end_time": "2023-02-20T10:58:36.984904Z", "start_time": "2023-02-20T10:58:36.706790Z" }, "execution": { "iopub.execute_input": "2024-06-14T15:01:40.585141Z", "iopub.status.busy": "2024-06-14T15:01:40.585055Z", "iopub.status.idle": "2024-06-14T15:01:40.705130Z", "shell.execute_reply": "2024-06-14T15:01:40.704937Z", "shell.execute_reply.started": "2024-06-14T15:01:40.585134Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "rel_err = N.abs((diff_CD(f, x0, dx) - dfdx(x0))/dfdx(x0))\n", "P.loglog(dx, rel_err)\n", "\n", "format_plot()" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "ExecuteTime": { "end_time": "2023-02-20T10:59:15.881479Z", "start_time": "2023-02-20T10:59:15.488550Z" }, "execution": { "iopub.execute_input": "2024-06-14T15:01:40.705497Z", "iopub.status.busy": "2024-06-14T15:01:40.705414Z", "iopub.status.idle": "2024-06-14T15:01:40.826771Z", "shell.execute_reply": "2024-06-14T15:01:40.826496Z", "shell.execute_reply.started": "2024-06-14T15:01:40.705490Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# porovnáme s asymptotickou hodnotou chyby\n", "err = N.abs(diff_CD_err(f, dfdx2, dfdx3, x0, dx)/dfdx(x0))\n", "P.loglog(dx, err,\":k\")\n", "\n", "format_plot()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Richardsonova extrapolace" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "ExecuteTime": { "end_time": "2023-02-20T11:07:27.078462Z", "start_time": "2023-02-20T11:07:26.776103Z" }, "execution": { "iopub.execute_input": "2024-06-14T15:01:40.827913Z", "iopub.status.busy": "2024-06-14T15:01:40.827817Z", "iopub.status.idle": "2024-06-14T15:01:40.954995Z", "shell.execute_reply": "2024-06-14T15:01:40.954694Z", "shell.execute_reply.started": "2024-06-14T15:01:40.827905Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# zkusme aplikovat Richardsonovu extrapolaci na obě metody, a poté zkusme odečíst\n", "# první čtyři členy asymptotického chybového rozvoje\n", "def richardson(f, x0, dx, p):\n", " if len(p) > 1:\n", " return (2**p[0]*richardson(f, x0, dx, p[1:]) -\\\n", " richardson(f, x0, 2*dx, p[1:]))/(2**p[0]-1)\n", " return (2**p[0]*operator(f, x0, dx) - operator(f, x0, 2*dx))/(2**p[0]-1)\n", "\n", "for operator, p1 in [(diff_FD, [1]), (diff_CD, [2]), (diff_CD, [2, 4, 6, 8])]:\n", " rel_err = N.abs((richardson(f, x0, dx, p1) - dfdx(x0))/dfdx(x0))\n", " P.loglog(dx, rel_err,\"--\")\n", " \n", "format_plot()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Vskutku můžeme snadno získat metodu 10. řádu přesnosti, i když možná nebude nejefektivnější." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Poznámka\n", "\n", "při odvozování nám může pomoct počítač, konkrétně knihovna sympy\n", "\n", "www.sympy.org" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "ExecuteTime": { "end_time": "2023-02-20T11:10:03.030625Z", "start_time": "2023-02-20T11:10:02.727567Z" }, "execution": { "iopub.execute_input": "2024-06-14T15:01:40.955333Z", "iopub.status.busy": "2024-06-14T15:01:40.955249Z", "iopub.status.idle": "2024-06-14T15:01:41.177466Z", "shell.execute_reply": "2024-06-14T15:01:41.177164Z", "shell.execute_reply.started": "2024-06-14T15:01:40.955326Z" } }, "outputs": [], "source": [ "from sympy import *\n", "x, y, z, t = symbols('x y z t')\n", "f = symbols('f', cls=Function)\n", "h, u = symbols(\"h u\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Rozvoj funkce do Taylorovy řady:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "ExecuteTime": { "end_time": "2023-02-20T11:10:05.074692Z", "start_time": "2023-02-20T11:10:04.880400Z" }, "execution": { "iopub.execute_input": "2024-06-14T15:01:41.177879Z", "iopub.status.busy": "2024-06-14T15:01:41.177745Z", "iopub.status.idle": "2024-06-14T15:01:41.217271Z", "shell.execute_reply": "2024-06-14T15:01:41.217015Z", "shell.execute_reply.started": "2024-06-14T15:01:41.177871Z" } }, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle f{\\left(0 \\right)} + x \\left. \\frac{d}{d \\xi} f{\\left(\\xi \\right)} \\right|_{\\substack{ \\xi=0 }} + \\frac{x^{2} \\left. \\frac{d^{2}}{d \\xi^{2}} f{\\left(\\xi \\right)} \\right|_{\\substack{ \\xi=0 }}}{2} + \\frac{x^{3} \\left. \\frac{d^{3}}{d \\xi^{3}} f{\\left(\\xi \\right)} \\right|_{\\substack{ \\xi=0 }}}{6} + \\frac{x^{4} \\left. \\frac{d^{4}}{d \\xi^{4}} f{\\left(\\xi \\right)} \\right|_{\\substack{ \\xi=0 }}}{24} + \\frac{x^{5} \\left. \\frac{d^{5}}{d \\xi^{5}} f{\\left(\\xi \\right)} \\right|_{\\substack{ \\xi=0 }}}{120} + O\\left(x^{6}\\right)$" ], "text/plain": [ "f(0) + x*Subs(Derivative(f(xi), xi), xi, 0) + x**2*Subs(Derivative(f(xi), (xi, 2)), xi, 0)/2 + x**3*Subs(Derivative(f(xi), (xi, 3)), xi, 0)/6 + x**4*Subs(Derivative(f(xi), (xi, 4)), xi, 0)/24 + x**5*Subs(Derivative(f(xi), (xi, 5)), xi, 0)/120 + O(x**6)" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f(x).series(x, 0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Aproximace derivace metodou dopředných diferencí" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "ExecuteTime": { "end_time": "2023-02-20T11:11:18.709038Z", "start_time": "2023-02-20T11:11:18.593266Z" }, "execution": { "iopub.execute_input": "2024-06-14T15:01:41.217656Z", "iopub.status.busy": "2024-06-14T15:01:41.217571Z", "iopub.status.idle": "2024-06-14T15:01:41.272698Z", "shell.execute_reply": "2024-06-14T15:01:41.272511Z", "shell.execute_reply.started": "2024-06-14T15:01:41.217649Z" } }, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle f{\\left(x \\right)} + \\left(t - x\\right) \\left. \\frac{d}{d \\xi_{1}} f{\\left(\\xi_{1} \\right)} \\right|_{\\substack{ \\xi_{1}=x }} + \\frac{\\left(t - x\\right)^{2} \\left. \\frac{d^{2}}{d \\xi_{1}^{2}} f{\\left(\\xi_{1} \\right)} \\right|_{\\substack{ \\xi_{1}=x }}}{2} + \\frac{\\left(t - x\\right)^{3} \\left. \\frac{d^{3}}{d \\xi_{1}^{3}} f{\\left(\\xi_{1} \\right)} \\right|_{\\substack{ \\xi_{1}=x }}}{6} + \\frac{\\left(t - x\\right)^{4} \\left. \\frac{d^{4}}{d \\xi_{1}^{4}} f{\\left(\\xi_{1} \\right)} \\right|_{\\substack{ \\xi_{1}=x }}}{24} + \\frac{\\left(t - x\\right)^{5} \\left. \\frac{d^{5}}{d \\xi_{1}^{5}} f{\\left(\\xi_{1} \\right)} \\right|_{\\substack{ \\xi_{1}=x }}}{120} + O\\left(\\left(t - x\\right)^{6}; t\\rightarrow x\\right)$" ], "text/plain": [ "f(x) + (t - x)*Subs(Derivative(f(_xi_1), _xi_1), _xi_1, x) + (t - x)**2*Subs(Derivative(f(_xi_1), (_xi_1, 2)), _xi_1, x)/2 + (t - x)**3*Subs(Derivative(f(_xi_1), (_xi_1, 3)), _xi_1, x)/6 + (t - x)**4*Subs(Derivative(f(_xi_1), (_xi_1, 4)), _xi_1, x)/24 + (t - x)**5*Subs(Derivative(f(_xi_1), (_xi_1, 5)), _xi_1, x)/120 + O((t - x)**6, (t, x))" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f(t).series(t, x)" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "ExecuteTime": { "end_time": "2023-02-20T11:12:29.176465Z", "start_time": "2023-02-20T11:12:29.121263Z" }, "execution": { "iopub.execute_input": "2024-06-14T15:01:41.273058Z", "iopub.status.busy": "2024-06-14T15:01:41.272980Z", "iopub.status.idle": "2024-06-14T15:01:41.296852Z", "shell.execute_reply": "2024-06-14T15:01:41.296696Z", "shell.execute_reply.started": "2024-06-14T15:01:41.273052Z" } }, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\frac{h \\left. \\frac{d}{d \\xi_{1}} f{\\left(\\xi_{1} \\right)} \\right|_{\\substack{ \\xi_{1}=x }} + \\frac{h^{2} \\left. \\frac{d^{2}}{d \\xi_{1}^{2}} f{\\left(\\xi_{1} \\right)} \\right|_{\\substack{ \\xi_{1}=x }}}{2} + \\frac{h^{3} \\left. \\frac{d^{3}}{d \\xi_{1}^{3}} f{\\left(\\xi_{1} \\right)} \\right|_{\\substack{ \\xi_{1}=x }}}{6} + \\frac{h^{4} \\left. \\frac{d^{4}}{d \\xi_{1}^{4}} f{\\left(\\xi_{1} \\right)} \\right|_{\\substack{ \\xi_{1}=x }}}{24} + \\frac{h^{5} \\left. \\frac{d^{5}}{d \\xi_{1}^{5}} f{\\left(\\xi_{1} \\right)} \\right|_{\\substack{ \\xi_{1}=x }}}{120} + O\\left(h^{6}\\right)}{h}$" ], "text/plain": [ "(h*Subs(Derivative(f(_xi_1), _xi_1), _xi_1, x) + h**2*Subs(Derivative(f(_xi_1), (_xi_1, 2)), _xi_1, x)/2 + h**3*Subs(Derivative(f(_xi_1), (_xi_1, 3)), _xi_1, x)/6 + h**4*Subs(Derivative(f(_xi_1), (_xi_1, 4)), _xi_1, x)/24 + h**5*Subs(Derivative(f(_xi_1), (_xi_1, 5)), _xi_1, x)/120 + O(h**6))/h" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "(f(t).series(t, x).subs(t, x+h) - f(x))/h" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "ExecuteTime": { "end_time": "2023-02-20T11:12:36.639801Z", "start_time": "2023-02-20T11:12:36.623880Z" }, "execution": { "iopub.execute_input": "2024-06-14T15:01:41.297229Z", "iopub.status.busy": "2024-06-14T15:01:41.297142Z", "iopub.status.idle": "2024-06-14T15:01:41.303393Z", "shell.execute_reply": "2024-06-14T15:01:41.303232Z", "shell.execute_reply.started": "2024-06-14T15:01:41.297222Z" } }, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\left. \\frac{d}{d \\xi_{1}} f{\\left(\\xi_{1} \\right)} \\right|_{\\substack{ \\xi_{1}=x }} + \\frac{h \\left. \\frac{d^{2}}{d \\xi_{1}^{2}} f{\\left(\\xi_{1} \\right)} \\right|_{\\substack{ \\xi_{1}=x }}}{2} + \\frac{h^{2} \\left. \\frac{d^{3}}{d \\xi_{1}^{3}} f{\\left(\\xi_{1} \\right)} \\right|_{\\substack{ \\xi_{1}=x }}}{6} + \\frac{h^{3} \\left. \\frac{d^{4}}{d \\xi_{1}^{4}} f{\\left(\\xi_{1} \\right)} \\right|_{\\substack{ \\xi_{1}=x }}}{24} + \\frac{h^{4} \\left. \\frac{d^{5}}{d \\xi_{1}^{5}} f{\\left(\\xi_{1} \\right)} \\right|_{\\substack{ \\xi_{1}=x }}}{120} + O\\left(h^{5}\\right)$" ], "text/plain": [ "Subs(Derivative(f(_xi_1), _xi_1), _xi_1, x) + h*Subs(Derivative(f(_xi_1), (_xi_1, 2)), _xi_1, x)/2 + h**2*Subs(Derivative(f(_xi_1), (_xi_1, 3)), _xi_1, x)/6 + h**3*Subs(Derivative(f(_xi_1), (_xi_1, 4)), _xi_1, x)/24 + h**4*Subs(Derivative(f(_xi_1), (_xi_1, 5)), _xi_1, x)/120 + O(h**5)" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "_.expand()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "a metodou centrovaných diferencí" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "ExecuteTime": { "end_time": "2023-02-20T11:13:37.670057Z", "start_time": "2023-02-20T11:13:37.586715Z" }, "execution": { "iopub.execute_input": "2024-06-14T15:01:41.303809Z", "iopub.status.busy": "2024-06-14T15:01:41.303733Z", "iopub.status.idle": "2024-06-14T15:01:41.341398Z", "shell.execute_reply": "2024-06-14T15:01:41.341240Z", "shell.execute_reply.started": "2024-06-14T15:01:41.303802Z" }, "scrolled": true }, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\left. \\frac{d}{d \\xi_{1}} f{\\left(\\xi_{1} \\right)} \\right|_{\\substack{ \\xi_{1}=x }} + \\frac{h^{2} \\left. \\frac{d^{3}}{d \\xi_{1}^{3}} f{\\left(\\xi_{1} \\right)} \\right|_{\\substack{ \\xi_{1}=x }}}{6} + \\frac{h^{4} \\left. \\frac{d^{5}}{d \\xi_{1}^{5}} f{\\left(\\xi_{1} \\right)} \\right|_{\\substack{ \\xi_{1}=x }}}{120} + O\\left(h^{5}\\right)$" ], "text/plain": [ "Subs(Derivative(f(_xi_1), _xi_1), _xi_1, x) + h**2*Subs(Derivative(f(_xi_1), (_xi_1, 3)), _xi_1, x)/6 + h**4*Subs(Derivative(f(_xi_1), (_xi_1, 5)), _xi_1, x)/120 + O(h**5)" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "((f(t).series(t, x).subs(t, x+h) - f(t).series(t, x).subs(t, x-h))/(2*h)).expand()" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.12.3" } }, "nbformat": 4, "nbformat_minor": 4 }