Neumann boundary condition

Summary

A Neumann boundary condition prescribes the derivative of the unknown function in the direction normal to the boundary. For an ordinary differential equation on $[a, b]$, it fixes $y'(a)$ and $y'(b)$. For a partial differential equation on a domain, it fixes the outward normal derivative $\frac{\partial u}{\partial \nu}$ on the boundary, which is a flux. It is one of the three classical conditions in a boundary value problem, with the Dirichlet and Robin conditions. See the definition.