- #1

ognik

- 643

- 2

## Homework Statement

Hi - I'm on the last chapter of this book and am a bit stuck. I am given a very basic fortran program (code attached in the zip file) and asked to 'investigate its accuracy and stability, for various values of Δt and lattice spacings'. The program is an implementation of the equation recursion relation below (H is hermitian).

The second (and probably prime) part of the exercise says 'Incorporate sources or sinks along the lattice and study the solutions that arise when ∅ vanishes everywhere at t = 0

## Homework Equations

$$ {\phi}_{n+1}= \frac{1}{1+H\Delta t} \left[{\phi}^{n}{S}^{n}{\Delta t}\right] $$

## The Attempt at a Solution

Part 1:

I have run the program for various sets of values - and the output all looks so similar that I can't see anything to discuss. The errors reported are of a similar magnitude. Some combinations of input don't produce any output - but that is probably just a validation issue, as I say it is a simple program with no frills (so it doesn't reject 'forbidden' values, just doesn't do anything).

I have done similar exercises in previous chapters, and there was always lots to talk about, so I must be missing some subtlety here - could someone try and give me a clue or 2 please...

Part 2:

The text hasn't used the concept of sources/sinks before, but I think the PDE in question is similar to a diffusion equation so - please correct me - sources and sinks would be where there is inflow/outflow from the volume under study? And they are related to the S

^{n}term in the equation? Earlier in this chapter I did some exercises on discretization, so I am familiar with that and lattices, but I am clueless otherwise (this course is about computational physics and as it happens I won't do equations like this until next year, C'est la vie)