Experimental science is costly. For amateur scientists who want to contribute, the inexpensive alternative is theoretical and computational science. You can get started for nothin, and even if you go all-out, you might spend $1,000 for a powerful computer and $3,000 for the most powerful software.
Most of the problems that have exact solutions are linear. Unfortunately, nature seems to like nonlinear processes that are much more complicated. The only effective way to model such processes are by approximating a solution, and reducing the error so that your model is close enough to reality to be useful. Most of these approximations involve complicated and intricate calculations with lots of data points. It would be practically impossible to do these by hand. A computer is capable of doing these calculations with the appropriate programming.
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