Mixed boundary condition

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In mathematics, a mixed boundary condition (also called a Robin boundary condition) imposed on an ordinary differential equation or a partial differential equation give information about both the values of a function and the values of its derivative on the boundary of the domain. Mixed boundary conditions are a combination of Dirichlet boundary conditions and Neumann boundary conditions.

In the case of an ordinary differential equation, for example such as

\frac{d^2y}{dx^2} + 3 y = 1

on the interval \ [0,1], mixed boundary conditions take the form

\ \alpha y(0) + \beta y'(0) = 0
\ \gamma y(1) + \delta y'(1) = 0

where \ \alpha, \ \beta, \ \gamma, and \ \delta are given numbers.

Mixed boundary conditions are commonly used in solving Sturm-Liouville problems which appear in many contexts in science and engineering.

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