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! file: bratu2df90.f90
! to build a Python module, use this:
! $$ f2py -m bratu2df90 -c bratu2df90.f90
subroutine bratu2d (m, n, alpha, x, f)
!f2py intent(hide) :: m = shape(x,0)
!f2py intent(hide) :: n = shape(x,1)
integer :: m, n
real(kind=8) :: alpha
real(kind=8), intent(in), target :: x(m,n)
real(kind=8), intent(inout) :: f(m,n)
real(kind=8) :: hx, hy
real(kind=8), pointer, &
dimension(:,:) :: u, uN, uS, uE, uW
! setup 5-points stencil
u => x(2:m-1, 2:n-1) ! center
uN => x(2:m-1, 1:n-2) ! north
uS => x(2:m-1, 3:n ) ! south
uW => x(1:m-2, 2:n-1) ! west
uE => x(3:m, 2:n-1) ! east
! compute nonlinear function
hx = 1.0/(m-1) ! x grid spacing
hy = 1.0/(n-1) ! y grid spacing
f(:,:) = x
f(2:m-1, 2:n-1) = &
(2*u - uE - uW) * (hy/hx) &
+ (2*u - uN - uS) * (hx/hy) &
- alpha * exp(u) * (hx*hy)
end subroutine bratu2d
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