PROGRAM Gauss_Seidel
IMPLICIT NONE
! Declare Variables
Real, allocatable :: x(:),y(:),u(:,:), v(:,:),u_old(:,:)
Real:: h,tolerence,error
Integer:: i,j,JI,NI
h=0.01
JI=100
NI=173
error = 1.d0
tolerence = 10E-4
! Total number of space stepsize
allocate (x(0:JI),y(0:NI),u(0:JI+1,0:NI+1),v(0:JI+1,0:NI+1),u_old(0:JI+1,0:NI+1))
open(10,file='Gauss_Seidel.m') !Opening files in Matlab
!Initial Conditions
x(0)= 0
x(JI)= 1.0
y(0)= 0
y(NI)= SQRT(3.0)
do i=0,JI
do j=0,NI
x(i)= i*h ! x-axix, x starts from 0 to 1
y(j)= j*h ! y-axis y starts from 0 to SQRT(3.0)
u(i,j)= 0 ! Entire Boundary is zero
end do
end do
while (error .GT. tolerence) do ! To stop
do i=1, JI-1
do j=1,NI-1
u_old(i,j)= u(i,j) ! To store the old values
!Using 5-point scheme Formulae and rearranging the equation
v(i,j)= 0.25*(u(i+1,j)+u(i,j+1)+u(i-1,j)+u(i,j-1)+h**2)
end do
end do
do i=1, JI-1
do j=1, NI-1
u(i,j)= v(i,j) ! Giving the new values
end do
end do
error =0.d0 ! Now, error reading the value of zero
do i=1,JI-1
do j=1, NI-1
error = error + abs(u(i,j)- u_old(i,j)) ! To Stop
end do
end do
end do
!Print out the Approximate solution in matlab to get output and plot
write(10,*) 'x=['
do i=0, JI
write(10,*) x(i)
end do
write(10,*) ']'
write(10,*) 'y=['
do j=0,NI
write(10,*) y(j)
end do
write(10,*) ']'
write(10,*) 'u=['
do i=0, JI
do j=0,NI
write(10,*) u(i,j)
end do
end do
write(10,*) ']'
write(10,*) " contour(x, y, reshape(u, length(x), length(y)))" !Ploting diagram x,y,u
write(10,*) "xlabel('x'),ylabel('y'),legend('Approximate Gauss Seidel')"
close(10)
END PROGRAM Gauss_Seidel
