The calculations failed again, and it seems as if no good will ever come of these researches. There's something so utterly heartbreaking about spending so much time on things which never seem to work. It will work eventually, though, somehow and someway. Hopefully it won't take as long as the thesis work that lasted five years!
Numerics, numerics, numerics. In applied mathematics, you more often than not end up with systems of equations that you can't solve yourself, so you have to ask a computer to do the next best thing and solve it numerically. In other words, you give it a best guess, and it improves the guess for you in the form of a patchwork of numbers that fits the problem. It's not particularly elegant, but it gets the job done, if you can choose the right way to explain it to the computer. It's also very frustrating when it doesn't work...
The problem with computational mathematics is that it's so easy to get wrapped up in trying to fix the problem by experimentation with little bits of code instead of going back to the source and reading about how other people have done the same problem. Not everyone can be an instinctive numerical expert, so you learn from people who are. There's something going on with this problem, and it's difficult to quantify... Life would be much easier if it only involved watching excellent television series and enjoying wonderful books. How to determine the difficulty in an unstable numerical scheme? How?
Progress happens, but incrementally. Research progresses just a little at a time, and when successful changes just a handful of ideas at the very most. Oh, it's going to need a lot more reading, balanced against the time spent on this endless proofreading project!
Side notes: Watched 'The River Wild', and still don't understand all the fuss about Meryl Streep. Helen Hunt could act her into the ground without even trying. Strange days. It's almost a good movie, though. Almost.
O.
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