{ "metadata": { "name": "", "signature": "sha256:b27c4ae520783f229d26e9528e0bc0a80cbf4d9b71f93e895471a6407cff70f5" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "Okruhy ot\u00e1zek z NEVF138\n", "=======================\n", "\n", "+ Numerick\u00e1 derivace, dop\u0159edn\u00e9 diference, zp\u011btn\u00e9 diference, centr\u00e1ln\u00ed diference\n", "+ Odhad chyby Taylorov\u00fdm rozvojem, asymptotick\u00e9 chov\u00e1n\u00ed chyby, Richardsonova extrapolace\n", "+ Numerick\u00e1 integrace, obd\u00e9ln\u00edkov\u00e9 pravidlo, lichob\u011b\u017en\u00edkov\u00e9 pravidlo, glob\u00e1ln\u00ed vs. lok\u00e1ln\u00ed chyba\n", "+ Integrace ODR, Explicitn\u00ed vs. Implicitn\u00ed metody.\n", "+ Rungovy Kuttovy metody - nap\u0159 Eulerova metoda, Heunova metoda (explicitn\u00ed), Lichob\u011b\u017en\u00edkov\u00e1 metoda (implicitn\u00ed)\n", "+ Leap Frog\n", "+ Stabilita, vy\u0161et\u0159ov\u00e1n\u00ed stability - testovac\u00ed rovnice, tuh\u00e9 soustavy\n", "+ Integrace PDR - diskretizace metodou kone\u010dn\u00fdch diferenc\u00ed (metoda s\u00edt\u00ed)\n", "+ \u0158e\u0161en\u00ed okrajov\u00fdch \u00faloh - p\u0159\u00edm\u00e9 (Gaussova eliminace, LU dekompozice, Fourierova transformace), nep\u0159\u00edm\u00e9 (Relaxa\u010dn\u00ed metody - Jacobi, Gauss Seidel...)\n", "+ Matice druh\u00fdch diferenc\u00ed - vlastn\u00ed \u010d\u00edsla a vlastn\u00ed vektory kvalitativn\u011b\n", "+ Po\u010d\u00e1te\u010dn\u011b-okrajov\u00e9 \u00falohy (evolu\u010dn\u00ed rovnice) - \n", "+ FTCS (forward time, cetered space), Laxova(-Friedrichsova) metoda, Crank Nicolson a pou\u017eitelnost pro parabolick\u00e9 (dif\u00faze) a hyperbolick\u00e9 (advekce) probl\u00e9my\n", "+ Von Neumannova anal\u00fdza stability, Courant Friedrichs Lewyho podm\u00ednka, \n", "+ Stru\u010dn\u011b princip metody kone\u010dn\u00fdch prvk\u016f: PDR $\\to$ slab\u00e1 formulace $\\to$ diskretizace prostoru funkc\u00ed $\\to$ \u0159e\u0161en\u00ed lin. rovnic\n", "+ Podm\u00edn\u011bnost matice a jej\u00ed v\u00fdznam pro numerick\u00e9 metody" ] }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [] } ], "metadata": {} } ] }