By Prof. Henning Mittelbach (auth.)
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Extra resources for Simulationen in BASIC
Ein entsprechendes Programm muB zunachst im Intervall (Xl,X2) die beiden werte min (f) und max (f) bestimmen. Dann generiert die Zufallsfunktion Punkte (x,y) mit den obigen Eigenschaften, die jeweils hinsichtlich ihrer Lage liberprlift werden. Zeile 17~ des Programms INTEGRATION transformiert das Auszahlungsergebnis S auf den Integralwert w. 05. 3 Eine lohnende Wette Auf einer Party mit etlichen Personen N kann man die wette wagen, ob bei wenigstens zwei Personen der Geburtstag (Tag und Monat) zusammenfallt.
R = "; INT <10 * G / N) / 10;") 50 240 250 PRINT: PRINT "MITTL. 5 untersuchte Bewegungsanalogie kann auch zweidimensional betrachtet werden. In diesem Fall entsteht ein orthogonales Wegenetz (oder: Punktegitter) des Typs 2 3 4 5 Lange i 2 3 ? Breite k Ein gegebener Punkt (d,f) hat in diesem Netz vier elementare Bewegungsmoglichkeiten, sofern er sich nicht auf dem Rand oder gar in einer Ecke dieses Gitters befindet. ). Ein entsprechendes Programm benotigt kein Feld; man kann mit den Koordinaten des wandernden Punktes (x,y) rechnen: Am Anfang gilt x = d, Y = f.
I, , • II •••••••• .... '"" ", "':'~ .... ' .. I, .... ,:. '. '.. '. I, ":". , ••••••••••• '. ,':.. I, '. ' ' ". " I, " " I. I, '. 10 Aquarium und Epidemie Typisch fur das iterativ-numerische L6sen von DGLen y' = f(x,y) in den vorangegangenen Abschnitten war die Ubersetzung in eine Form mit dem Anfangswert (xo, YO). Diese sog. EULER-Methode (die aus der Sicht des Mathematikers noch durch KonvergenzUberlegungen erganzt werden muBte) ist auch in Stufen anwendbar, narnlich zum L8sen von DGLen h6herer Ordnung.