Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Finite differencing on non-uniform grids

  1. Oct 20, 2015 #1

    hunt_mat

    User Avatar
    Homework Helper

    Hi,

    Recently I had to find a derivative on a uniform grid. Being naive I tried the following scheme:
    [tex]f'(x_{n})=Af(x_{n+2})+Bf(x_{n+1})+Cf(x_{n})+Df(x_{n-1})+Ef(x_{n-2})[/tex]

    Then write the [itex]f(x_{n\pm i})[/itex] in terms of [itex]f^{(n)}(x_{n})[/itex] by use of Taylor's theorem. This lead to a system of linear equations for the A,B,C,D,E which required inverting a Vandermonde matrix.

    I tried it out a couple of times and it worked okay for the first derivative but when I applied it to higher derivatives it became unstable. Does anyone know what is going wrong?

    I also tried a seven point stencil in the same way and that bizarrely was even worse.

    Mat
     
  2. jcsd
  3. Oct 20, 2015 #2

    Geofleur

    User Avatar
    Science Advisor
    Gold Member

    It might be helpful to look at the actual matrix you get for a case that causes trouble. It's probably also a good idea to do this for the smallest system possible. If you can see the problem play out on a system you could compute by hand, it might well give you an idea about what's going wrong.
     
  4. Oct 20, 2015 #3

    hunt_mat

    User Avatar
    Homework Helper

    Possibly, but I have tested the 7 point stencil on simple examples and have not got the answers which I should have. The five point stencil however works relative well for first order derivatives but not on higher derivatives (I think)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Finite differencing on non-uniform grids
Loading...