CLS
DIM A(40,40)
DIM C(40)
DIM X(40)
PRINT "FREDHOLM INTEGRAL EQUATION"
PRINT "enter K and G IN subroutines"
PRINT
PRINT "VALUES OF A, B, AND N"
PRINT
INPUT "KEY IN A, THE LOWER LIMIT:     ";A
INPUT "KEY IN B, THE UPPER LIMIT:     ";B
INPUT "# OF INTERVALS (MUST BE EVEN): ";N
PRINT
PRINT
H = (B -A) /N
X = A
T = A
FOR I=1 TO N + 1
GOSUB [NIZEZE]
A(I,1) = K
IF I <> 1 THEN [TWZEZE]
A(I,1) = 1 + K
[TWZEZE]
X = X + H
NEXT I
T = A + H
FOR J = 2 TO N
X = A
FOR I = 1 TO N + 1
GOSUB [NIZEZE]
IF INT(J / 2)* 2 <> J THEN [THTHZE]
A(I,J) = 4 * K
IF I= J THEN [THONZE]
GOTO [THSEZE]
[THONZE]
A(I,J) = 1 + 4 * K
GOTO [THSEZE]
[THTHZE]
A(I,J) = 2 * K
IF I = J THEN [THSIZE]
GOTO [THSEZE]
[THSIZE]
A(I,J) = 1 + 2 * K
[THSEZE]
X = X + H
NEXT I
T = T + H
NEXT J
X = A
T = B
FOR I = 1 TO N + 1
GOSUB [NIZEZE]
A(I,N + 1) = K
GOSUB [NITWZE]
C(I) = G
IF I <> N + 1 THEN [FONIZE]
A(I,N + 1) = 1 + K
[FONIZE]
X = X + H
NEXT I
FOR Z = 1 TO N + 1
A(Z,N + 2) = C(Z)
NEXT Z
N = N + 1
M = N + 1
L = N -1
FOR K = 1 TO L
JJ = K
B1 = ABS(A(K,K))
KP = K + 1
FOR I = KP TO N
A1 = ABS(A(I,K))
IF (B1-A1) >= 0 THEN [SIONZE]
B1 = A1
JJ = I
[SIONZE]
NEXT I
IF (JJ -K) = 0 THEN [SISEZE]
FOR J = K TO M
TE = A(JJ,J)
A(JJ,J) = A(K,J)
A(K,J) = TE
NEXT J
[SISEZE]
FOR I = KP TO N
QU = A(I,K) / A(K,K)
FOR J = KP TO M
A(I,J)= A(I,J) -QU * A(K,J)
NEXT J
NEXT I
FOR I = KP TO N
A(I,J) = 0
NEXT I
NEXT K
X(N)= A(N,M) / A(N,N)
FOR NN = 1 TO L
SU = 0
I = N -NN
IP = I + 1
FOR J = IP TO N
SU = SU + A(I,J) * X(J)
NEXT J
X(I)=(A(I,M)-SU) / A(I,I)
NEXT NN
PRINT
X = A
FOR I = 1 TO N
PRINT "X =    ";X
PRINT "F(X) = ";X(I)
PRINT
X = X + H
NEXT I
GOTO [NIFOZE]
[NIZEZE]
REM ENTER K HERE ****************
K = 2 * H *LOG(X* X + T * T) / 3
REM *****************************
RETURN
[NITWZE]
REM ENTER G HERE ****************
G = 4 + SIN(.5 * X)
REM *****************************
RETURN
[NIFOZE]
END