Cauchy boundary condition

In mathematics, a Cauchy (French: ) boundary condition 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 condition. It is named after the prolific 19th-century French mathematical analyst Augustin Louis Cauchy. In mathematics, a Cauchy (French: ) boundary condition 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 condition. 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, where, in order to ensure that a unique solution y ( s ) {displaystyle y(s)} exists, one may specify the value of the function y {displaystyle y} and the value of the derivative y ′ {displaystyle y'} at a given point s = a {displaystyle s=a} , i.e.,