Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 
 

 

A fundamental solution for a biharmonic finite-difference operator


Author: R. Bruce Simpson
Journal: Math. Comp. 21 (1967), 321-339
MSC: Primary 65.66
DOI: https://doi.org/10.1090/S0025-5718-1967-0226880-X
MathSciNet review: 0226880
Full-text PDF Free Access

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • [1] J. H. Bramble & B. E. Hubbard, ``On the formulation of finite difference analogues of the Dirichlet problem for Poisson's equation,'' Numer. Math., v. 4, 1962, pp. 313-327. MR 26 #7157. MR 0149672 (26:7157)
  • [2] J. H. Bramble & B. E. Hubbard, ``A priori bounds on the discretization error in the numerical solution of the Dirichlet problem,'' Contributions to Differential Equations, Vol. 2, 1963, pp. 229-251. MR 26 #7158. MR 0149673 (26:7158)
  • [3] R. J. Duffin & D. H. Shaffer, ``Asymptotic expansion of double Fourier transforms,'' Duke Math. J., v. 27, 1960, pp. 581-596. MR 22 #8280. MR 0117501 (22:8280)
  • [4] L. V. Kantorovich & V. I. Krylov, Approximate Methods of Higher Analysis, Interscience, New York; Noordhoff, Groningen, 1958. MR 21 #5268. MR 0106537 (21:5268)
  • [5] P. Laasonen, ``On the solution of Poisson's difference equation,'' J. Assoc. Comput. Mach., v. 5, 1958, pp. 370-382. MR 22 #12726. MR 0121999 (22:12726)
  • [6] M. Mangad, ``Bounds for the two-dimensional discrete harmonic Green's function,'' Math. Comp., v. 20, 1966, pp. 60-67. MR 0198701 (33:6856)
  • [7] W. H. McCrea & F. J. W. Whipple, ``Random paths in two and three dimensions,'' Proc. Roy. Soc. Edinburgh, v. 60, 1940, pp. 281-298. MR 2, 107 MR 0002733 (2:107f)
  • [8] R. B. Simpson, Finite Difference Methods for Two Biharmonic Boundary Value Problems, Ph.D. Thesis, University of Maryland, 1966.

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65.66

Retrieve articles in all journals with MSC: 65.66


Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1967-0226880-X
Article copyright: © Copyright 1967 American Mathematical Society

American Mathematical Society