Dirichlet-to-Neumann map ($\Lambda :g\mapsto {\partial }_{n}u$)

Given a uniquely solvable Dirichlet problem, this map sends prescribed Dirichlet boundary data to the solution's outward normal derivative. It depends on the differential operator and domain. Spectral global relations offer one way to compute it numerically from boundary traces, while a finite collocation scheme still requires a rank and conditioning check.