Boundary Conditions

There are three types of boundary conditions commonly encountered in the solution of partial differential equations:

1. Dirichlet boundary conditions specify the value of the function on a surface T=f(r,t).

2. Neumann boundary conditions specify the normal derivative of the function on a surface,

 (partialT)/(partialn)=n^^·del T=f(r,t).

3. Robin boundary conditions. For an elliptic partial differential equation in a region Omega, Robin boundary conditions specify the sum of alphau and the normal derivative of u=f at all points of the boundary of Omega, with alpha and f being prescribed.

See also

Boundary Value Problem, Cauchy Conditions, Dirichlet Boundary Conditions, Goursat Problem, Initial Conditions, Initial Value Problem, Neumann Boundary Conditions, Partial Differential Equation, Robin Boundary Conditions

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Arfken, G. Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 502-504, 1985.Morse, P. M. and Feshbach, H. "Boundary Conditions and Eigenfunctions." Ch. 6 in Methods of Theoretical Physics, Part I. New York: McGraw-Hill, pp. 495-498 and 676-790, 1953.

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Boundary Conditions

Cite this as:

Weisstein, Eric W. "Boundary Conditions." From MathWorld--A Wolfram Web Resource.

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