E:/turkuaz/krylov/codes/newton/1.2b/physics/bratu/anaJ/f.f90

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!bratu problem
subroutine f(X,func,n)
use localParameters
implicit none
integer i,j,k,n,z
integer index
real(8) X(n),func(n)
real(8) dx,dy




! call index from the index matrix and mesh info!!!!


dx=(Lx)/(nx-1.d0)
dy=(Ly)/(ny-1.d0)




func=0.d0
! in this problem, boundaries are all homogenous Dirichlet boundary conditions
! as a result, "func=X" initialization below is enough for boundary info.
! boundary definitions are still added (but commented-out) as being a template
! for other problems

func=X

!bottom boundary 

j=1     
z=(j-1)*nx
do i=1,nx
        index=(z+i-1)*unk+1
        func(index)=X(index)
end do

!top boundary 

j=ny     
z=(j-1)*nx
do i=1,nx
        index=(z+i-1)*unk+1
        func(index)=X(index)
end do


!left boundary 

i=1     

do j=2,ny-1
        index=((j-1)*nx+i-1)*unk+1
        func(index)=X(index)
end do

!right boundary 

i=nx     

do j=2,ny-1
        index=((j-1)*nx+i-1)*unk+1
        func(index)=X(index)
end do


! interior


do j=2,ny-1
        
        z=(j-1)*nx

        do i=2,ny-1
                
                index=(z+i-1)*unk+1


                func(index)=(X(index-unk) -2.d0*X(index) + X(index+unk))/dx**2.d0 + (X(index-nx*unk) -2.d0*X(index) + X(index+nx*unk))/dy**2.d0 + lambda*dexp(X(index))



        end do



end do



end subroutine f

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