Boundary Conditions
There are several types of boundary conditions commonly encountered in the solution of Partial DifferentialEquations.
- 1. Dirichlet Boundary Conditions specify the value of the function on a surface
. - 2. Neumann Boundary Conditions specify the normal derivative of the function on a surface,
- 3. Cauchy Boundary Conditions specify a weighted average of first and second kinds.
- 4. Robin Boundary Conditions. For an elliptic partial differential equation in a region
, Robin boundaryconditions specify the sum of 
and the normal derivative of 
at all points of the boundary of , with 
and 
being prescribed.
References
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.