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  2. Neumann boundary condition - Wikipedia

    en.wikipedia.org/wiki/Neumann_boundary_condition

    It is possible to describe the problem using other boundary conditions: a Dirichlet boundary condition specifies the values of the solution itself (as opposed to its derivative) on the boundary, whereas the Cauchy boundary condition, mixed boundary condition and Robin boundary condition are all different types of combinations of the Neumann and ...

  3. Dirichlet boundary condition - Wikipedia

    en.wikipedia.org/wiki/Dirichlet_boundary_condition

    The question of finding solutions to such equations is known as the Dirichlet problem. In the sciences and engineering, a Dirichlet boundary condition may also be referred to as a fixed boundary condition or boundary condition of the first type. It is named after Peter Gustav Lejeune Dirichlet (1805–1859). [1]

  4. Poincaré–Steklov operator - Wikipedia

    en.wikipedia.org/wiki/Poincaré–Steklov_operator

    The values of the temperature on the surface is the Dirichlet boundary condition of the Laplace equation, which describes the distribution of the temperature inside the body. The heat flux through the surface is the Neumann boundary condition (proportional to the normal derivative of the temperature).

  5. Dirichlet problem - Wikipedia

    en.wikipedia.org/wiki/Dirichlet_problem

    The next steps in the study of the Dirichlet's problem were taken by Karl Friedrich Gauss, William Thomson (Lord Kelvin) and Peter Gustav Lejeune Dirichlet, after whom the problem was named, and the solution to the problem (at least for the ball) using the Poisson kernel was known to Dirichlet (judging by his 1850 paper submitted to the ...

  6. Mixed boundary condition - Wikipedia

    en.wikipedia.org/wiki/Mixed_boundary_condition

    Green: Neumann boundary condition; purple: Dirichlet boundary condition. In mathematics, a mixed boundary condition for a partial differential equation defines a boundary value problem in which the solution of the given equation is required to satisfy different boundary conditions on disjoint parts of the boundary of the domain where the condition is stated.

  7. Neumann–Poincaré operator - Wikipedia

    en.wikipedia.org/wiki/Neumann–Poincaré_operator

    Exterior Dirichlet problem. Since 1 is not in the range of T K − ½I, f can be written uniquely as f = T K φ − φ/2 + λ where φ is unique up to a constant. Then u = D(φ) + λS(ψ) gives the solution of the Dirichlet problem in Ω c by the jump formula. Interior Neumann problem. The condition (f,1) = 0 implies that f = T K *φ −

  8. Boundary conditions in fluid dynamics - Wikipedia

    en.wikipedia.org/wiki/Boundary_conditions_in...

    Showing wall boundary condition. The most common boundary that comes upon in confined fluid flow problems is the wall of the conduit. The appropriate requirement is called the no-slip boundary condition, wherein the normal component of velocity is fixed at zero, and the tangential component is set equal to the velocity of the wall. [1]

  9. Eigenvalues and eigenvectors of the second derivative

    en.wikipedia.org/wiki/Eigenvalues_and...

    2.4 Mixed Dirichlet-Neumann boundary conditions 2.5 Mixed Neumann-Dirichlet boundary conditions 3 Derivation of Eigenvalues and Eigenvectors in the Discrete Case