8900  DEF FNF()=3*+2*Y-Z
9000  REM  *****  DEZ20R *****  MATHEMATICS PROGRAM  *****
9001  REM  *****  VERSION 1  *****  7/31/69  *****
9002  REM  INITIAL VALUE PROBLEM
9003  READ X0,Y,Z,B,H,L
9004  LET X=X0
9005  LET E=1/L
9006  IF (B-X0)*H>0 THEN 9008
9007  LET H=-H
9008  IF (B-X0)*L>0 THEN 9010
9009  LET L=-L
9010  REM
9011  PRINT "VALUE OF X","VALUE OF Y","VALUE OF Y'"
9012  PRINT 
9013  PRINT X,Y,Z
9014  GOTO 9025
9015  LET P1=Y+H*Z
9016  LET Q1=Z+H*FNF(X)
9017  LET Y=(Y+P1)/2+.5*H*Q1
9018  LET Y1=Y
9019  LET Z1=Z
9020  LET Y=P1
9021  LET Z=Q1
9022  LET X=X+H
9023  LET Z=(Z1+Q1)/2+H/2*FNF(X)
9024  LET Y=Y1
9025  IF (X+H-B)*SGN(L)+1.E-07 >= 0 THEN 9028
9026  LET R=X+H
9027  GOTO 9029
9028  LET R=B
9029  LET A=INT(E*R)/E+L*(SGN(H)-1)/2
9030  IF (A+L-R)*SGN(L)-1.E-07 >= 0 THEN 9032
9031  LET A=A+L
9032  IF (X-A)*SGN(L)+1.E-07 >= 0 THEN 9035
9033  LET Q=A
9034  GOSUB 9041
9035  IF R=B THEN 9037
9036  GOTO 9015
9037  IF ABS(R-A)<.5*.000001 THEN 9040
9038  LET Q=R
9039  GOSUB 9041
9040  STOP 
9041  LET P2=Y+(Q-X)*Z
9042  LET Q2=Z+(Q-X)*FNF(X)
9043  LET Y2=(Y+P2)/2+.5*(Q-X)*Q2
9044  LET Y1=Y
9045  LET Z1=Z
9046  LET Y=P2
9047  LET Z=Q2
9048  LET Z2=(Z1+Q2)/2+(Q-X)/2*FNF(Q)
9049  LET Y=Y1
9050  LET Z=Z1
9051  PRINT Q,Y2,Z2
9052  RETURN 
9053  STOP 
9900  DATA 0,0,1,5,.01,.1
9999  END 
