keybd INPUT yes screen home lf swiss13 on %j,%y 100 nolist fmt \n\N:=\F\n yes 1 yes fixed 2 degrees off 27520.00 27500.00 10.00 -10.12 10 10 j,y a 1 h step size constant... how far in the x direction do we go each iteration. 0.05 home This is the home cell for a demonstration of a numerical solution to the differential equation describing simple harmonic motion: y''= -a*y To execute the demonstration, put initial values into cells y and yp, then position to the home cell, and choose Execute from the Special menu. This example computes successive values of y and yp (y') with third order accuracy. The Runge-Kutta formulae come from "Advanced Calulus For Engineers", by F.B. Hildebrandt, Prentice Hall, 1949. These formulae are summarized below: a:= h:=0.05 home:=j! yold! ypold! y! yp! j:=j+1 k1:=h*ypold k1p:=-a*h*yold k2:=h*(ypold+k1p!/2) k2p:=-a*h*(yold+k1!/2) k3:=h*(ypold+2*k2p!-k1p!) k3p:=-a*h*(yold+2*k2!-k1!) y:=yold+(k1!+4*k2!+k3!)/6 yold:=y yp:=ypold+(k1p!+4*k2p!+k3p!)/6 ypold:=yp 9.93 j 27520.00 k1 0.49 k1p 0.08 k2 0.50 k2p 0.07 k3 0.50 k3p 0.06 y y is the displacement variable in the simple harmonic motion. -1.11 yold -1.60 yp 9.93 ypold 9.86