Being able to check if the numerical solution of an ordinary differential equation makes sense.
Moreover, depending on th inherent structure of the differential equation, they know what integrator should be chosen.
Initial- and boundary value problems for ordinary and partial differential equations: One-step and multi-step methods, adaptivity, structure perserving integrators.
Introduction to numerical methods for partial differential equations.
Analysis, linear algebra, numerical mathematics.
Knowledge of ODEs is advantageous but not necessary.