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Mixed Boundary Condition




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

:
rac{d^2y}{dx^2} + 3 y = 1


on the interval \ {Link without Title} , 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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