!!!!!!!!!!!!!!!!!!!!!!!!!!! Program 3.C !!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! !
! Please Note: !
! !
! (1) This computer program is written by Tao Pang in conjunction with !
! his book, "An Introduction to Computational Physics," published !
! by Cambridge University Press in 1997. !
! !
! (2) No warranties, express or implied, are made for this program. !
! !
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!
PROGRAM WAVE
!
! Program for the eigenvalue problem with a combination of the
! bisection method and the Numerov algorithm for u" = -k**2*u
! with boundary conditions u(0)=u(1)=0.
! Copyright (c) Tao Pang 1997.
!
IMPLICIT NONE
INTEGER, PARAMETER :: N=101
INTEGER :: I,ISTEP
REAL :: DL,H,AK,BK,DK,EK,F0,F1
REAL, DIMENSION (N) :: Q,S,U
!
! Initialization of the problem
!
DL = 1.0E-06
H = 1.0/(N-1)
AK = 2.0
BK = 4.0
DK = 1.0
EK = AK
U(1) = 0.0
U(2) = 0.01
ISTEP = 0
!
DO I = 1,N
S(I) = 0.0
Q(I) = EK*EK
END DO
CALL NMRV (N,H,Q,S,U)
F0 = U(N)
!
! Bisection method for the root
!
DO WHILE (ABS(DK).GT.DL)
EK = (AK+BK)/2.0
DO I = 1,N
Q(I) = EK*EK
END DO
CALL NMRV (N,H,Q,S,U)
F1 = U(N)
IF ((F0*F1).LT.0) THEN
BK = EK
DK = BK-AK
ELSE
AK = EK
DK = BK-AK
F0 = F1
END IF
ISTEP = ISTEP+1
END DO
WRITE (6,"(I4,3F16.8)") ISTEP,EK,DK,F1
END PROGRAM WAVE
!
SUBROUTINE NMRV (N,H,Q,S,U)
!
! The Numerov algorithm for the equation u"(x)+q(x)u(x)=s(x)
! as given in Eqs. (3.77)-(3.80) in the book.
! Copyright (c) Tao Pang 1997.
!
IMPLICIT NONE
INTEGER, INTENT (IN) :: N
INTEGER :: I
REAL, INTENT (IN) :: H
REAL :: G,C0,C1,C2,D,UTMP
REAL, INTENT (IN), DIMENSION (N) :: Q,S
REAL, INTENT (INOUT), DIMENSION (N) :: U
!
G = H*H/12.0
!
DO I = 2, N-1
C0 = 1.0+G*((Q(I-1)-Q(I+1))/2.0+Q(I))
C1 = 2.0-G*(Q(I+1)+Q(I-1)+8.0*Q(I))
C2 = 1.0+G*((Q(I+1)-Q(I-1))/2.0+Q(I))
D = G*(S(I+1)+S(I-1)+10.0*S(I))
UTMP = C1*U(I)-C0*U(I-1)+D
U(I+1) = UTMP/C2
END DO
END SUBROUTINE NMRV