Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

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

 
 

 

Finite difference methods for the computation of the ``Poisson kernel'' of elliptic operators


Author: Pierre Jamet
Journal: Math. Comp. 22 (1968), 477-488
MSC: Primary 65.66
DOI: https://doi.org/10.1090/S0025-5718-1968-0250499-9
MathSciNet review: 0250499
Full-text PDF

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] R. Courant, K. O. Friedrichs & H. Lewy, ``Über die partiellen Differenzengleichungen der mathematischen Physik,'' Math. Ann., v. 100, 1928, pp. 32-74; English transl., New York University Courant Inst. Math. Sciences Research Dept., N. Y. 0.-7689.
  • [3] G. E. Forsythe & W. R. Wasow, Finite-Difference Methods for Partial Differential Equations, Wiley, New York, 1960. MR 23 #B3156. MR 0130124 (23:B3156)
  • [4] P. Jamet, Numerical Methods and Existence Theorems for Singular Linear Boundary-Value Problems, Thesis, University of Wisconsin, 1967.
  • [5] P. Jamet, Theorie des Barrières Discrètes et Applications à des Problèmes Linéaires Élliptiques du ``Type de Dirichlet,'' Rapport CEA - R 3214, Commissariat à l'Energie Atomique, Paris, 1967.
  • [6] P. Jamet & S. V. Parter, ``Numerical methods for elliptic differential equations whose coefficients are singular on a portion of the boundary,'' SIAM J. Numer. Anal., v. 4, 1967, no. 2. MR 0215543 (35:6383)
  • [7] W. V. Koppenfels, Über die Existenz der Lösungen linearer partieller Differentialgleichungen vom elliptischen Typus, Dissertation, Göttingen, 1929.
  • [8] I. G. Petrovsky, ``New proof of the existence of a solution of Dirichlet's problem by the method of finite differences,'' Uspehi Mat. Nauk, v. 8, 1941, pp. 161-170. (Russian) MR 3, 123.
  • [9] W. Rudin, Real and Complex Analysis, McGraw-Hill, New York, 1966. MR 0210528 (35:1420)

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/S0025-5718-1968-0250499-9
Article copyright: © Copyright 1968 American Mathematical Society

American Mathematical Society