human
Why do we need to solve PDEs in order to solve ODEs?
assistant
The reason is that ODEs are linear, while PDEs are nonlinear. If you want to solve an ODE, you can use a numerical method to approximate the solution. For example, Euler’s method is a very simple method that can be used to approximate the solution to a first-order ODE. However, this method is only valid if the initial condition is smooth, which is not the case for many types of ODEs.