A fundamental solution for a biharmonic finitedifference operator
Author:
R. Bruce Simpson
Journal:
Math. Comp. 21 (1967), 321339
MSC:
Primary 65.66
MathSciNet review:
0226880
Fulltext PDF Free Access
References 
Similar Articles 
Additional Information
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J.
H. Bramble and B.
E. Hubbard, On the formulation of finite difference analogues of
the Dirichlet problem for Poisson’s equation, Numer. Math.
4 (1962), 313–327. MR 0149672
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J.
H. Bramble and B.
E. Hubbard, A priori bounds on the discretization error in the
numerical solution of the Dirichlet problem, Contributions to
Differential Equations 2 (1963), 229–252. MR 0149673
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J. Duffin and D.
H. Shaffer, Asymptotic expansion of double Fourier transforms,
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Moshe
Mangad, Bounds for the twodimensional
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0198701 (33 #6856), http://dx.doi.org/10.1090/S00255718196601987014
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R. B. Simpson, Finite Difference Methods for Two Biharmonic Boundary Value Problems, Ph.D. Thesis, University of Maryland, 1966.
 [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. 313327. 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. 229251. 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. 581596. 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. 370382. MR 22 #12726. MR 0121999 (22:12726)
 [6]
 M. Mangad, ``Bounds for the twodimensional discrete harmonic Green's function,'' Math. Comp., v. 20, 1966, pp. 6067. 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. 281298. 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.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0025571819670226880X
PII:
S 00255718(1967)0226880X
Article copyright:
© Copyright 1967
American Mathematical Society
