High accuracy finite difference approximation to solutions of elliptic partial differential equations.

@article{Lynch1978HighAF,
  title={High accuracy finite difference approximation to solutions of elliptic partial differential equations.},
  author={Robert E. Lynch and J. D. Rice},
  journal={Proceedings of the National Academy of Sciences of the United States of America},
  year={1978},
  volume={75 6},
  pages={2541-4}
}
A flexible finite difference method is described that gives approximate solutions of linear elliptic partial differential equations, Lu = G, subject to general linear boundary conditions. The method gives high-order accuracy. The values of the unknown approximation function U are determined at mesh points by solving a system of finite difference equations L(h)U = I(h)G. L(h)U is a linear combination of values of U at points of a standard stencil (9-point for two-dimensional problems, 27-point… CONTINUE READING
Highly Cited
This paper has 18 citations. REVIEW CITATIONS

From This Paper

Figures, tables, results, connections, and topics extracted from this paper.
13 Extracted Citations
9 Extracted References
Similar Papers

Citing Papers

Publications influenced by this paper.
Showing 1-10 of 13 extracted citations

Referenced Papers

Publications referenced by this paper.
Showing 1-9 of 9 references

0(h ) accurate finite difference approximation to solutions of the Poisson equation in three variables

  • R. E. Lynch
  • Purdue University Department of Computer Science…
  • 1977
1 Excerpt

Nine - point difference solutions for Poisson ' s equation

  • O. B. Rosser
  • Corap . & Maths , with Appls .
  • 1975

Nine-point difference solutions for Poisson's equation, Corap

  • O. B. Rosser
  • Maths, with Appls.,
  • 1975

Optimal few - point discretizations of linear source problems , SIAM 0

  • G. Birkhoff, S. Gulati
  • Numer . Anal . TJ
  • 1975

Optimal few-point discretizations of linear source problems

  • G. Birkhoff, S. Gulati
  • SIAM 0. Numer. Anal. TJ_
  • 1975

Approximation of the Bessel eigenvalue problem by finite differences

  • H. L. Dershem
  • SIAM J. Numer. Analy
  • 1971

Dauwalder, Discrete representations of partial differential operators, in Errors in Digitial Computation, Vol. 2, edited by L.B. Rail

  • D. M. Young, J.H
  • 1965

Krylov, Approximation Methods of Higher Analysis, Noordoff-Interscience

  • L. V. Kantorovich, V.I
  • 1958

Discrete representations of partial differential operators

  • D. M. Young, J. H. Dauwalder
  • Errors in Digitial Computation

Similar Papers

Loading similar papers…