Simulating Turing machines with {O,P}DEs.

ODEs are good enough. Your comment got me started digging.

I believe that the reference is to seminal work of Pour-El and Richards where they measure the computational contents of various types of classical systems of partial differential equations. They have a series of papers where they carry this out; I believe much of it can be found in their book Computability in analysis and physics (Perspectives in Mathematical Logic, Springer-Verlag, 1989). There are other approaches to this, but they all reach essentially the same conclusions. Pour-El and Richards have the advantage that they concentrate on specific systems that actually arise in physics, such as the wave equation.