!!!!!!!!!!!!!!!!!!!!!!!!!!! Program 8.1 !!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! !
! 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 GALERKIN
!
! This program solves the one-dimensional Poisson equation with the
! Galerkin method as described in the text. Copyright (c) Tao Pang 1997.
!
IMPLICIT NONE
INTEGER, PARAMETER :: N=99
INTEGER :: I
REAL :: PI,XL,H,D,E,B0,B1,XIM,XI,XIP
REAL, DIMENSION (N) :: B,A,Y,W,U
!
PI = 4.0*ATAN(1.0)
XL = 1.0
H = XL/(N+1)
D = 2.0/H
E = -1.0/H
B0 = PI/H
B1 = 1.0/H
!
! Find the elements in L and U
!
W(1) = D
U(1) = E/D
DO I = 2, N
W(I) = D-E*U(I-1)
U(I) = E/W(I)
END DO
!
! Assign the array B
!
DO I = 1, N
XIM = H*(I-1)
XI = H*I
XIP = H*(I+1)
B(I) = B0*COS(PI*XI)*(XIM+XIP-2.0*XI) &
+B1*(2.0*SIN(PI*XI)-SIN(PI*XIM)-SIN(PI*XIP))
END DO
!
! Find the solution
!
Y(1) = B(1)/W(1)
DO I = 2, N
Y(I) = (B(I)-E*Y(I-1))/W(I)
END DO
!
A(N) = Y(N)
DO I = N-1,1,-1
A(I) = Y(I)-U(I)*A(I+1)
END DO
!
WRITE (6,"(2F16.8)") (I*H,A(I), I=1,N)
END PROGRAM GALERKIN