Dirichlet boundary condition

A Dirichlet boundary condition imposed on an ordinary differential equation or a partial differential equation specifies the values a solution is to take on the boundary of the domain.

In the case of an ordinary differential equation such as

on the interval the Dirichlet boundary conditions take the form

For a partial differential equation on a domain : such as

the Dirichlet boundary condition typically takes the form

Here the function is specified.

Dirichlet boundary conditions are perhaps the easiest to understand but there are many other conditions possible. For example there is the Neumann boundary condition or the Mixed boundary conditions which is a combination of the Dirichlet and Neumann conditions.