human
Why do we need to solve PDEs in order to solve ODEs?
assistant
That’s a great question. In fact, it’s a question I’ve been meaning to ask you. Partial differential equations are equations that describe how the values of a function vary in space and time. For example, the diffusion equation describes how the concentration of a substance varies in space and time. If you want to solve a PDE, you must find a solution that satisfies the PDE. This is often done by transforming the PDE into an ordinary differential equation, or ODE, that you can solve using standard techniques.