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Ever since my introduction to computational fluid dynamics last year, I’ve been reading several calc books and tutorials to learn Partial Differential Equations. By no stretch of the imagination am I a master, but last night I finally succeded in solving the Heat Equation.

Not only do I now understand initial and boundary conditions, but I used them with a numerical method for the heat equation in a C program. The image below shows heat change on a 1-dimensional level (a rod, say) for some length of time. At the left you see that the rod is hot in the middle and cool at the ends, and the farther right you go (therefore as time passes) it cools. Perhaps this isn’t the best illustration of the Heat Equation’s great uses, but it’s a start.

After pouring through equations for several weeks, I was quite relieved last night to find that the numerical method for solving the equation really is nothing more than a glorified average, each cell sharing heat with its neighbors. I’m going to work on making some real world simulations and see how well my code works.