First, their algorithm advances a solution forward in time by solving the heat equation (also called the "diffusion equation"), which models how heat from a source spreads over a shape.

Linear and quasilinear first order PDE. The method of characteristics. Conservation laws and propagation of shocks. Basic theory for three classical equations of mathematical physics (in all spatial ...

For instance, the rate of heat flow can be modeled using an equation very similar to that governing the speed of particle diffusion. Another example involves wave equations, which apply to the ...