Well I have completed the first stage of the analysis, the linear and weakly nonlinear cases. I just have to make the notation a little more clear and that should be a part of a chapter for my thesis which is nice. I may add a little bit on the numerics and then I am sorted, I can go on to what could possibly be my “main” problem where I can get some serious maths done.
Speaking of numerics though, I finally figured out where my bug was and as I suspected it was something simple. I used an equation to pick out the correct variable in my array and that is where the problem was. I have since used an if elseif statement which works beautifully. I have some rather dull number crunching to get some pretty looking waves.