Skip to main content
Log in

On the formulation of finite difference analogues of the Dirichlet problem for Poisson's equation

  • Published:
Numerische Mathematik Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. Collatz, L.: Bemerkungen zur Fehlerabschätzung für das Differenzenverfahren bei partiellen Differentialgleichungen. A. angew. Math. Mech.13, 56–57 (1933).

    Google Scholar 

  2. —: Numerical treatment of differential equations, 3rd ed. Berlin-Göttingen-Heidelberg: Springer 1960.

    Google Scholar 

  3. Courant, R., K. Friedrichs andH. Lewy: Über die partiellen Differenzengleichungen der mathematischen Physik. Math. Ann.100, 32–74 (1928).

    Google Scholar 

  4. Forsythe, G., andW. Wasow: Finite-difference methods for partial differential equations. New York: Wiley 1960.

    Google Scholar 

  5. Gerschgorin, S.: Fehlerabschätzung für das Differenzenverfahren zur Lösung partieller Differentialgleichungen. Z. angew. Math. Mech.10, 373–382 (1930).

    Google Scholar 

  6. Kantorovich, L., andV. Krylov: Approximate Methods of Higher Analysis. Netherlands: Noordhoff Ltd. 1958.

    Google Scholar 

  7. Laasonen, P.: On the degree of convergence of discrete approximations for the solutions of the Dirichlet problem. Ann. Acad. Sci. Fenn. A. I.246, 1–19 (1957).

    Google Scholar 

  8. —: On the solution of Poisson's difference equation. J. Assoc. Comput. Mach.5, 370–382 (1958).

    Google Scholar 

  9. Motzkin, T., andW. Wasow: On the approximation of linear elliptic differential equations by difference equations with positive coefficients. J. Math. Phys.31, 253–259 (1953).

    Google Scholar 

  10. Shortley, G., andR. Weller: The numerical solution of Laplace's equation. J. Appl. Phys.9, 334–348 (1938).

    Google Scholar 

  11. Walsh, J., andD. Young: On the accuracy of the numerical solution of the Dirichlet problem by finite differences. J. Res. Nat. Bur. Stand.51, 343–363 (1953).

    Google Scholar 

  12. ——: On the degree of convergence of solutions of difference equations to the solution of the Dirichlet problem. J. Math. Phys.33, 80–93 (1954).

    Google Scholar 

  13. Wasow, W.: On the truncation error in the solution of Laplace's equation by finite differences. J. Res. Nat. Bur. Stand.48, 345–348 (1952).

    Google Scholar 

  14. —: The accuracy of difference approximations to plane Dirichlet problems with piecewise analytic boundary values. Quart. Appl. Math.15, 53–63 (1957).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

This research was supported in part by the United States Air Force through the Air Force Office of Scientific Research of the Air Research and Development Command under Contract No. AF 49(638)-228.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bramble, J.H., Hubbard, B.E. On the formulation of finite difference analogues of the Dirichlet problem for Poisson's equation. Numer. Math. 4, 313–327 (1962). https://doi.org/10.1007/BF01386325

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01386325

Keywords

Navigation