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In mathematics, a Cauchy 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. ==Second order ordinary differential equations== Cauchy boundary conditions are simple and common in second order ordinary differential equations, : where, in order to ensure that a unique solution exists, one may specify the value of the function and the value of the derivative at a given point , i.e., : and : where is a boundary or initial point. Since the parameter is usually time, Cauchy conditions can also be called ''initial value conditions'' or ''initial value data'' or simply ''Cauchy data''. An example of such a situation is Newton's laws of motion where the acceleration depends on position , velocity , and the time ; here, Cauchy data corresponds to knowing the initial position and velocity. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Cauchy boundary condition」の詳細全文を読む スポンサード リンク
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