stencil in finite difference

alecrimi

Hi
Sorry for the stupid question, but what is exactly a "stencil" in finite difference methods ?
Is the results of the expansion points ?
Cheers
Alex

hunt_mat

This is also called a computational molecule in some texts, it basically is the recurrence relation that you use to calculate the next point in your calculation, so for example a stencil for the Euler method for the ODE [itex]\frac{du}{dx}=f(x,u)[/itex] would be:
[tex]
u_{n+1}=u_{n}+hf(x_{n},u_{n})
[/tex]
For PDEs it would be something more complicated. I hope you get the general idea.