Boundary Value Problem

A boundary value problem is a problem, typically an Ordinary Differential Equation or a Partial Differential Equation, which has values assigned on the physical boundary of the Domain in which the problem is specified. For example,

$$\cases{ {\partial^2u\over \partial t^2}-\nabla^2u = f & in ... ...rtial u\over \partial t}(0,t) = u_2 & on $\partial\Omega$,\cr}$$

where $\partial\Omega$ denotes the boundary of $\Omega$, is a boundary problem.

See also Boundary Conditions, Initial Value Problem

References

Eriksson, K.; Estep, D.; Hansbo, P.; and Johnson, C. Computational Differential Equations. Lund: Studentlitteratur, 1996.

Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. ``Two Point Boundary Value Problems.'' Ch. 17 in Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England: Cambridge University Press, pp. 745-778, 1992.