a boundary-value problem is a differential equation subjected to constraints called boundary conditions. A solution to a boundary value problem is a...

In mathematics, some boundary value problems can be solved using the methods of stochastic analysis. Perhaps the most celebrated example is Shizuo Kakutani's...

elliptic boundary value problem is a special kind of boundary value problem which can be thought of as the steady state of an evolution problem. For example...

together with some boundary conditions at extreme values of x {\displaystyle x} . The goals of a given Sturm–Liouville problem are: To find the λ for...

satisfy on the boundary; ideally so as to ensure that a unique solution exists. A Cauchy boundary condition specifies both the function value and normal derivative...

for solving a boundary value problem by reducing it to an initial value problem. It involves finding solutions to the initial value problem for different...

interior of a given region that takes prescribed values on the boundary of the region. The Dirichlet problem can be solved for many PDEs, although originally...

the domain. A Cauchy problem can be an initial value problem or a boundary value problem (for this case see also Cauchy boundary condition). It is named...

calculus, an initial value problem (IVP) is an ordinary differential equation together with an initial condition which specifies the value of the unknown function...

solutions of this equation. A concrete example would be an elliptic boundary-value problem like ( ∗ ) L u := − Δ u + h ( x ) u = f in  Ω , {\displaystyle (*)\qquad...

solution that has a finite number of points. FEM formulation of a boundary value problem finally results in a system of algebraic equations. The method approximates...

In mathematics, a free boundary problem (FB problem) is a partial differential equation to be solved for both an unknown function u {\displaystyle u} and...

a Stefan problem is a particular kind of boundary value problem for a system of partial differential equations (PDE), in which the boundary between the...

Rescale the original boundary value problem by replacing t {\displaystyle t} with τ ε {\displaystyle \tau \varepsilon } , and the problem becomes 1 ε y ″ (...

problem is one of the 23 Hilbert problems set out in a celebrated list compiled in 1900 by David Hilbert. It asks whether all boundary value problems...

of Green's functions in mathematics is to solve non-homogeneous boundary value problems. In modern theoretical physics, Green's functions are also usually...

Schwarz, solves a boundary value problem for a partial differential equation approximately by splitting it into boundary value problems on smaller domains...

of boundary value problems. The method divides the interval over which a solution is sought into several smaller intervals, solves an initial value problem...

specifies the values of the derivative applied at the boundary of the domain. It is possible to describe the problem using other boundary conditions: a...

"quasilinearization" is commonly used when the differential equation is a boundary value problem. Quasilinearization replaces a given nonlinear operator N with a...

In mathematics, a mixed boundary condition for a partial differential equation defines a boundary value problem in which the solution of the given equation...

semimajor axis of the conic. Stated another way, Lambert's problem is the boundary value problem for the differential equation r ¨ = − μ r ^ r 2 {\displaystyle...

two-point (or, in the case of a complex problem, a multi-point) boundary-value problem. This boundary-value problem actually has a special structure because...

shown above with classical polarization states. A common type of boundary value problem is (to put it abstractly) finding a function y that satisfies some...

Boundary conditions in fluid dynamics are the set of constraints to boundary value problems in computational fluid dynamics. These boundary conditions...

methods for IVPs, and remark that boundary value problems (BVPs) require a different set of tools. In a BVP, one defines values, or components of the solution...

the Dirichlet and Neumann boundary value problems for the Laplacian in a bounded domain in the plane with smooth boundary. The methods use the theory...

least/stationary action. Many important problems involve functions of several variables. Solutions of boundary value problems for the Laplace equation satisfy...

their associated boundary value problems in mathematics, Lagrange's identity, named after Joseph Louis Lagrange, gives the boundary terms arising from...

or measurement purposes. The boundary problem occurs because of the loss of neighbors in analyses that depend on the values of the neighbors. While geographic...