10 PRINT "REG-FAL EXAMPLE OF ARTIFICIAL DERIVATIVE METHOD OF NEWTON-RAPHSON": PRINT
20 DEFINT I: CLEAR
30 DEF FNY (DY) = DY ^ 2 - Y1 ^ 2 - 2! * Y1 * (V1 * DY - Q2) ^ 2 / (G * DY * (DY - Y1))
40 READ V1, Y1, Q2, G, Y, DYY
50 DATA 3.,2.,4.,9.806,29.,1E-4: PRINT "V1,Y1,Q2,G,Y,DYY="; V1Y1; Q2; G; Y; DYY
60 F = FNY(Y): OY = Y - DYY: OF = FNY(OY): FF = F - OF: YY = Y - OY: TOL = .5 * DYY
70 FOR I = 1 TO 15
80 IF (ABS(FF) > 0!) AND (ABS(YY) >= TOL) THEN YN = Y - F * YY / FF ELSE GOTO 110
90 OY = Y: Y = YN: OF = F: YY = Y - OY: F = FNY(Y): FF = F - OF: PRINT Y
100 NEXT I
110 PRINT : PRINT "Y2="; : PRINT USING "    ###.###   "; Y