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  2. Boundary value problem - Wikipedia

    en.wikipedia.org/wiki/Boundary_value_problem

    A boundary condition which specifies the value of the function itself is a Dirichlet boundary condition, or first-type boundary condition. For example, if one end of an iron rod is held at absolute zero, then the value of the problem would be known at that point in space. A boundary condition which specifies the value of the normal derivative ...

  3. Dirichlet boundary condition - Wikipedia

    en.wikipedia.org/wiki/Dirichlet_boundary_condition

    In mathematics, the Dirichlet boundary condition is imposed on an ordinary or partial differential equation, such that the values that the solution takes along the boundary of the domain are fixed. The question of finding solutions to such equations is known as the Dirichlet problem .

  4. Cauchy boundary condition - Wikipedia

    en.wikipedia.org/wiki/Cauchy_boundary_condition

    Cauchy boundary conditions are simple and common in second-order ordinary differential equations, ″ = ((), ′ (),), where, in order to ensure that a unique solution () exists, one may specify the value of the function and the value of the derivative ′ at a given point =, i.e.,

  5. Neumann boundary condition - Wikipedia

    en.wikipedia.org/wiki/Neumann_boundary_condition

    In mathematics, the Neumann (or second-type) boundary condition is a type of boundary condition, named after Carl Neumann. [1] When imposed on an ordinary or a partial differential equation , the condition specifies the values of the derivative applied at the boundary of the domain .

  6. Robin boundary condition - Wikipedia

    en.wikipedia.org/wiki/Robin_boundary_condition

    Robin boundary conditions are commonly used in solving Sturm–Liouville problems which appear in many contexts in science and engineering. In addition, the Robin boundary condition is a general form of the insulating boundary condition for convection–diffusion equations. Here, the convective and diffusive fluxes at the boundary sum to zero:

  7. Method of images - Wikipedia

    en.wikipedia.org/wiki/Method_of_images

    The method of images (or method of mirror images) is a mathematical tool for solving differential equations, in which boundary conditions are satisfied by combining a solution not restricted by the boundary conditions with its possibly weighted mirror image. Generally, original singularities are inside the domain of interest but the function is ...

  8. Stefan problem - Wikipedia

    en.wikipedia.org/wiki/Stefan_problem

    To close the mathematical system a further equation, the Stefan condition, is required. This is an energy balance which defines the position of the moving interface. Note that this evolving boundary is an unknown (hyper-)surface; hence, Stefan problems are examples of free boundary problems.

  9. Green's function - Wikipedia

    en.wikipedia.org/wiki/Green's_function

    In mathematics, a Green's function (or Green function) is the impulse response of an inhomogeneous linear differential operator defined on a domain with specified initial conditions or boundary conditions. This means that if is a linear differential operator, then