A FINITE DIFFERENCE SCHEME FOR THE NEUMANN AND THE DIRICHLET PROBLEM
- Author
- Friedrichs, K. O.
- Published
- United States : [publisher not identified], 1962.
[Oak Ridge, Tennessee] : [U.S. Atomic Energy Commission], 1962. - Physical Description
- microopaque : positive ; 8 x 13 cm
- Summary
- A specific feature of the finite difference scheme proposed is that in it the boundary condition and the differential equation are treated simultaneously. The scheme results from a variational principle of the original differential equation problem, simply by using the Ritz method employing piecewise linear approximation functions. Thus a rather uniform treatment of boundary condition and differential equation will result. The coefficients of the substitute boundary condition will be given as the areas of sections of triangles cut out by the boundary; they are therefore not sensitive to variations of the direction of the boundary. An advantage of the approach is that the mean convergence of the solutions of the difference equations (including first difference quotients) to that of the differential equation is implied by the general theory and requires no special proof. Whether or not the scheme is useful in actual computation is still to be seen. The scheme for the Neumann problem of Laplace's equation is first described; then its extension to systems of second order is discussed. A lower estimate is given for the eigenvalues of the matrix involved. The method for extending the scheme to the Dirichlet problem is indicated. (auth)
- Report Numbers
- NYO-9760
- Other Subject(s)
- Collection
- U.S. Atomic Energy Commission depository collection.
- Note
- DOE contract number: AT(30-1)-1480
NSA number: NSA-17-008701
OSTI Identifier 4731808
Research organization: New York Univ., New York. Atomic Energy Commission Computing and Applied Mathematics Center.
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