How to approach a Poisson's Equation of a square domain

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As someone with severe Asperger's I can't understand programming and after 100s of hours trying to learn it just doesn't click.

I am looking for any suggestions on material to learn to solve an equation such as

Poisson equation on a square domain of 51 by 51

$$U_(xx_) + U_(yy_) = xy $$

$$(0,y)=0; (x, 0)=0; _(51,y)=; u_n(x, 51)=y$$