Cauchy boundary condition

In mathematics, a Cauchy ([koˈʃi]) boundary conditions augments an ordinary differential equation or a partial differential equation with conditions that the solution must satisfy on the boundary; ideally so to ensure that a unique solution exists. A Cauchy boundary condition specifies both the function value and normal derivative on the boundary of the domain. This corresponds to imposing both a Dirichlet and a Neumann boundary conditions. It is named after the prolific 19th-century French mathematical analyst Augustin Louis Cauchy.

Cauchy boundary conditions are simple and common in second-order ordinary differential equations,