Abstract
Two methods for solving the biharmonic equation are compared. One method is direct, using eigenvalue-eigenvector decomposition. The other method is iterative, solving a Poisson equation directly at each iteration.
- 1 Smith, J. The coupled equation approach to the numerical solution of the biharmonic equation by finite differences, I. SIAM J. Num. Anal 5 (1970), 104-111.Google ScholarCross Ref
- 2 Ehrlich, L.W. Solving the biharmonic equation as coupled finite difference equations. SIAM J. Num. Anal. 8 (1971), 278-287.Google ScholarCross Ref
- 3 Ehrlich, L.W. Coupled harmonic equations, SOR, and Chebyshev acceleration. M.O.C. 26 (1970), 335-343.Google Scholar
- 4 Ehrlich, L.W. Point and block SOR applied to a coupled set of difference equations. APL/JHU TG-1166, 1971.Google Scholar
- 5 Golub, G.H. An algorithm for the discrete biharmonic equation. Personal communication.Google Scholar
- 6 Hockney, R.W. A fast direct solution of Poisson's equation using Fourier analysis. J. ACM 12, 1 (Jan. 1965), 95-113. Google ScholarDigital Library
- 7 Hockney, R.W. The potential calculation and some applications. Methods in Computat. Physics 9 (1970), 135-211.Google Scholar
- 8 Buzbee, B.L., Golub, G.H., and Nielson, C.W. On direct methods for solving Poisson's equation. SlAM J. Num. Anal. 7 (1970), 627-656.Google ScholarCross Ref
- 9 Colony, R., and Reynolds, R.R. An application of Hockney's method for solving Poisson's equation. Proc. AFIPS 1970 SJCC, Vol. 36, AFIPS Press, Montvale, N.J., pp. 409-416.Google Scholar
- 10 Householder, A.S. The Theory of Matrices in Numerical Analysis. Blaisdell Pub. Co., New York, 1964.Google Scholar
- 11 Young, D. lterative Solution of Large Linear Systems. Academic Press, New York, 1971.Google Scholar
- 12 McLaurin, Johnnie William. A general coupled equation approach for solving the biharmonic boundary value problem. Dept. of Math., UCLA, Los Angeles, Calif., 1971.Google Scholar
- 13 Gupta Murli Manohar. Convergence and stability of finite difference schemes for some elliptic equations. Ph.D. Diss., Dept. of Math., U. of Saskatchewan, Saskatoon, Saskatchewan, Canada, Aug. 1971. (See also On numerical solution of biharmonic equation by splitting. M.M. Gupta and R. Manohar in Proc. Manitoba Conf. on Num. Math., U. of Manitoba, Winnipeg, Manitoba, Canada, Oct. 7-9, 1971.)Google Scholar
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