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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,

 {(partial^2u)/(partialt^2)-del ^2u=f   in Omega; u(0,t)=u_1   on partialOmega; (partialu)/(partialt)(0,t)=u_2   on partialOmega,
(1)

where partialOmega denotes the boundary of Omega, is a boundary problem.


See also

Boundary Conditions, Initial Value Problem

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References

Eriksson, K.; Estep, D.; Hansbo, P.; and Johnson, C. Computational Differential Equations. Lund: Studentlitteratur, 1996.Powers, D. L. Boundary Value Problems, 4th ed. San Diego, CA: Academic Press, 1999.Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. "Two Point Boundary Value Problems" and "Boundary Values Problems." Ch. 17 and part of §19.0 in Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England: Cambridge University Press, pp. 753-787 and 829-833, 1992.

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Boundary Value Problem

Cite this as:

Weisstein, Eric W. "Boundary Value Problem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/BoundaryValueProblem.html

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