fortran - Difference of finite difference solution between two timesteps -

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i have solution discretized differential equation given by

f(i)

where i spatial index. how can find difference between solution @ each adjacent time step? more clear:

the solution defined array

real,dimension(0:10) :: f

i discretize differential equation , solve stepping forward in time. if time index k, portion of code 

do k=1,25    = 1,10       f(i) = f(i+1)+f(i-1)+f(i)    end end

i can print solution, f(i) @ each time step k following code

print*, "print f(i) k=, k print "(//(5(5x,e22.14)))", f

how can find difference between solution @ each adjacent time step? is, time steps k+1,k. store value in new array g, has dimension given by

real,dimension(0:10) :: g

so trying find 

!g(i)=abs(f(i;k+1)-f(i;k))...not correct code.

how can this? way implement code? not sure how using if /then statements or whatever code need needed this. thanks

typically, in explicit time integration methods or iterative methods, have save last time-step last solution, current time-step solution , possibly more.

so have 

  real,dimension(0:10) :: f0, f

where f0 previous value

you iterate jacobi or gauss-seidel discretization:

f = f0  k=1,25     = 1,9       f(i) = f(i+1)+f(i-1)+f(i)    end     max_diff = maxval(abs(f-f0))     if (diff small enough) exit     f0 = f  end

if have time-evolving problem heat equation:

f = f0  k=1,25     = 1,9       f(i) = f0(i) + dt * viscosity * (f0(i+1)+f0(i-1)+f0(i))    end     max_diff = maxval(abs(f-f0))     f0 = f  end

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