Definition: Boundary conditions, which exist in the form of mathematical equations, exert a set of additional constraints to the problem on specified boundaries. The concept of boundary conditions applies to both ordinary and partial differential equations.

There are five types of boundary conditions: Dirichlet, Neumann, Robin, Mixed, and Cauchy, within which Dirichlet and Neumann are predominant. The Dirichlet, Neumann, and Robin are also called the first-type, second-type and third-type boundary condition respectively.

The mixed boundary condition refers to the cases in which Dirichlet boundary conditions are prescribed in some parts of the boundary while Neumann boundary conditions exist in the others. While being less common, Cauchy boundary conditions are also used in second-order differential equations, correspond to imposing a Dirichlet and a Neumann boundary conditions simultaneously.