Dirichlet Boundary Conditions
Get Dirichlet Boundary Conditions essential facts below. View Videos or join the Dirichlet Boundary Conditions discussion. Add Dirichlet Boundary Conditions to your PopFlock.com topic list for future reference or share this resource on social media.
Dirichlet Boundary Conditions

In mathematics, the Dirichlet (or first-type) boundary condition is a type of boundary condition, named after Peter Gustav Lejeune Dirichlet (1805-1859).[1] When imposed on an ordinary or a partial differential equation, it specifies the values that a solution needs to take along the boundary of the domain.

The question of finding solutions to such equations is known as the Dirichlet problem. In applied sciences, a Dirichlet boundary condition may also be referred to as a fixed boundary condition.

Examples

ODE

For an ordinary differential equation, for instance,

the Dirichlet boundary conditions on the interval [a,b] take the form

where ? and ? are given numbers.

PDE

For a partial differential equation, for example,

where ?2 denotes the Laplace operator, the Dirichlet boundary conditions on a domain ? ? Rn take the form

where f is a known function defined on the boundary ??.

Applications

For example, the following would be considered Dirichlet boundary conditions:

Other boundary conditions

Many other boundary conditions are possible, including the Cauchy boundary condition and the mixed boundary condition. The latter is a combination of the Dirichlet and Neumann conditions.

See also

References

  1. ^ Cheng, A. and D. T. Cheng (2005). Heritage and early history of the boundary element method, Engineering Analysis with Boundary Elements, 29, 268-302.

  This article uses material from the Wikipedia page available here. It is released under the Creative Commons Attribution-Share-Alike License 3.0.

Dirichlet_boundary_conditions
 



 



 
Music Scenes