CLS
REM == PREDICTOR/CORRECTOR ==
REM INPUT DATA
GOSUB [FIFOZE]
REM == INITIALIZE VARIABLES AND STARTING VALUES==
[THZE]
GOSUB [ONZENIZE]
REM == PREDICTOR ==
[FOZE]
GOSUB [ONFOZEZE]
N = 0
REM == CORRECTOR ==
[SIZE]
GOSUB [ONFOTHZE]
REM == CHECK FOR TOLERANCE ==
D = Z(2) -Z(1)
D = ABS(D)/H4
IF D < E2 THEN [ONFOZE]
REM ==DIFFERENCE TOO LARGE, APPLY CORRECTOR AGAIN ==
REM APPLY CORRECTOR AGAIN
N = N + 1
IF N >= N0 THEN [TWEIZE]
Z(1) = Z(2)
GOTO [SIZE]
REM == CONVERGENCE ATTAINED ==
[ONFOZE]
X0 = X0 + H
Y0 = Z(2)
PRINT" X = ";X0;" Y = ";Y0
Z0 = X0
W0 = Y0
IF X0 >= B THEN [FITHZE]
FOR I =1 TO 3
F(I)= F(I + 1)
NEXT I
X = X0
Y = Y0
F(4) = FNF(X,Y)
IF C$= "Y" THEN [FOZEZE]
GOTO [FOZE]
[TWEIZE]
IF C$ = "N" THEN [FOSEZE]
PRINT
PRINT "N0 CONVERGENCE: STEP HALVED"
PRINT
H = H / 2
PRINT"H = ";H
PRINT
PRINT "RE- START AT X = ";Z0
PRINT
X0 = Z0
Y0 = W0
GOTO [THZE]
[FOZEZE]
IF D > El THEN [FOZE]
PRINT
PRINT "TOO MUCH PRECISION: STEP DOUBLED"
PRINT
H = 2 * H
PRINT "H = ";H
GOTO [THZE]
[FOSEZE]
PRINT
PRINT "*** ERROR ***"
PRINT
PRINT "NO CONVERGENCE ATTAINED"
PRINT
PRINT "WITHIN SPECIFIED TOLERANCE"
[FITHZE]
END
REM ==PRINT TITLE PAGE==
[FIFOZE]
PRINT
PRINT "PREDICTOR-CORRECTOR METH0D"
PRINT "FOR A FIRST ORDER EQUATION"
PRINT
PRINT
PRINT "ENTER INTERVAL OF INTEGRATION"
PRINT
REM ==INPUT DATA==
INPUT "A = ";A
INPUT "B = ";B
PRINT
PRINT "INITIAL CONDITION"
PRINT
INPUT "YA = ";Y0
PRINT
PRINT "WANT STEPSIZE CONTROL (Y/N) ";
INPUT C$
PRINT
PRINT "INITIAL STEPSIZE"
PRINT
INPUT "H = ";H0
PRINT
INPUT "TOLERANCE OF LOCAL ERROR X AS IN 1e-X = ";E2
E2=1/10^E2
PRINT
PRINT "MAXIMUM NUMBER OF "
PRINT
PRINT "CORRECTION CYCLES ";
INPUT N0
PRINT
PRINT
PRINT "SOLUTION"
PRINT "********"
PRINT
REM ==INITIALIZE VARIABLES==
H = H0
X0 = A
Z0 = X0
W0 = Y0
REM == El IS LOWER BOUND FOR LOCAL ERROR==
E1 = E2 / 1000
RETURN
REM ==INITIALIZE VALUES FOR STARTING PROCEDURE==
[ONZENIZE]
PRINT
X = X0
Y = Y0
Z0 = X0
W0 = Y0
H2 = H / 24
H4 = H * 14
F(1)=FNF(X,Y)
REM ==4TH ORDER RUNGE-KUTTA METH0D TO COMPUTE STARTING VALUES==
U = X0
W = Y0
FOR I = 1 TO 3
X = U
Y = W
K1 = H * FNF(X,Y)
X = U + 0.5 * H
Y = W + 0.5 * K1
K2 = H * FNF(X,Y)
Y = W + 0.5 * K2
K3 = H * FNF(X,Y)
X = U + H
Y = W + K3
K4 = H * FNF(X,Y)
U = U + H
W = W + (K1 + 2 * K2 + 2 * K3 + K4) / 6
PRINT "X = ";U;"  Y =";W
Y = W
F(I+ 1) = FNF(X,Y)
NEXT I
X0 = U
Y0 = W
RETURN
REM == 4TH ORDER ADAMS -BASHFORT==
REM == METH0D (EXPLICIT) ==
[ONFOZEZE]
Q = 55 * F(4) -59 * F(3) + 37 * F(2) -9 * F(1)
Z(1) = Y0 + H2 * Q
RETURN
REM == CORRECTED VALUE ==
REM == 4TH ORDER ADAMS -MOULTON ==
[ONFOTHZE]
X = X0 + H
Y = Z(1)
F(5) = FNF(X,Y)
Q = 9*F(5)+19*F(4)-5*F(3)+F(2)
Z(2)= Y0+H2*Q
REM ************ ENTER FN HERE ****************
FUNCTION FNF(X,Y)
FNF=X+Y
END FUNCTION
REM *******************************************