CLS
PRINT
PRINT "RUNGE-KUTTA METH0D FOR A "
PRINT "SYSTEM OF EQUATIONS"
PRINT
PRINT
REM ==INPUT DATA==
PRINT
PRINT "ENTER LIMITS OF INTEGRATION"
PRINT
INPUT "A = ";A
PRINT
INPUT "B = ";B
PRINT
INPUT "YA = ";Y0
PRINT
PRINT "INITIAL STEPSIZE "
INPUT "H = ";H0
PRINT
PRINT "LOCAL ERROR TOLERANCE X AS IN 1E-X"
INPUT "X = ";E1
E1 = 1/10^E1
PRINT
PRINT "STEPSIZE CONTROL (Y/N) ";
INPUT C$
PRINT
PRINT "SOLUTION"
PRINT "********"
PRINT
REM ==INITIALIZE VARIABLES==
X0 = A
H = H0
E5 = E1 / 100
REM ==OUTPUT RESULTS==
[FOONZE]
PRINT
PRINT "X = ";X0;"   Y = ";Y0
GOSUB [FOEIZE]
REM ==CHECKFOR END OFINTERVAL==
IF X0 <= B THEN [FOONZE]
PRINT
PRINT "END OF EXECUTION"
GOTO [ONZEZEZE]
REM ==INTERGRATION ROUTINE==
REM ==NEXT POINT W/CURRENT STEP SIZE==
[FOEIZE]
U = X0
W = Y0
T = H
GOSUB [EIZEZE]
Q1 = W
T2 = H
REM==NEXTPOINT W/ HALF STEP SIZE==
[FIFOZE]
U = X0
W = Y0
T = T2 / 2
FOR I = 1 TO 2
GOSUB [EIZEZE]
Z(I) = W
NEXT I
Q2 = Z(2)
REM ==CHECK FOR CONVERGENCE==
Q3 = (Q2 -Q1) / 15
D = ABS(Q3)/ T2
IF D < E1 THEN [SEFOZE]
REM ==OUT OF TOLERANCE==
IF C$= "Y"THEN [SEONZE]
REM ==ABORT EXECUTION==
PRINT
PRINT "** ERROR **CONVERGENCY NOT"
PRINT "ATTAINED WITHIN TOLERANCE"
PRINT "FOR STEP SIZE H=";H;" AT X=";X0
PRINT "TRY AGAIN USING STEPSIZE CONTROL"
GOTO [ONZEZEZE]
PRINT
REM ==CONVERGENCE NOT ATTAINED-HALF STEP SIZE==
[SEONZE]
Q1 = Z(1)
T2 = T2 / 2
REM ==ITERATE AGAIN==
GOTO [FIFOZE]
REM ==CONVERGENCE ATTAINED==
REM ==RICHARDSON EXTRAPOLATION==
[SEFOZE]
Y0 = Q2 + Q3
X0 = X0 + T2
IF C$ = "N" THEN [EIZEZE]
REM ==DOUBLE STEP SIZE IF TOO SMALL==
IF D > E5 THEN [EIZEZE]
H = 2 * H
RETURN
[EIZEZE]
X = U
REM ==4TH ORDER RUNGE-KUTTA=
Y = W
K1 = FNF(X,Y)
K1 = T * K1
X = U + T / 2
Y = W + K1 / 2
K2 =FNF(X,Y)
K2 = T * K2
Y = W + K2 / 2
K3= FNF(X,Y)
K3 = T * K3
X = U + T
Y = W + K3
K4 = FNF(X,Y)
K4 = T * K4
V1 = K1 + 2 * K2 + 2 * K3 + K4
W = W + V1 / 6
U = X
RETURN
REM ************ PLACE FUNCTION HERE **********
FUNCTION FNF(X,Y)
FNF=X+Y
END FUNCTION
[ONZEZEZE]
END