Boundary Value Problem
A differential equation together with a set of additional constraints, called boundary conditions, specified at the boundaries of the domain.
Governing formula
Dirichlet: y(a)=y_A; Neumann: y'(a)=y'_A; Robin: α y(a) + β y'(a) = γ
SI unit
Differential Equation Condition
In depth
Dirichlet conditions specify field values on boundaries; Neumann conditions specify normal derivative fluxes; Robin conditions combine both. Common in electrostatics, heat conduction, and quantum mechanics.
Examples in the real world
Finding electrostatic potential V inside a conductor cage with specified boundary potential values.