say I'm incrementing and at some defined value. I should have a 2D grid with and down either side and the central values will be .
How do I calculate ?
Is it simply
where is defined as
I'm not sure what you want here. u is simply some function that is defined at each node of grid. is the value of that function at the i,j-node. It is NOT a derivative, it is the function itself. is an approximation to on that grid and, similarly, is an approximation to .