Skip to main content
Log in

General multistep finite difference methods for the solution ofu xy =f(x, y, u, u x ,u y )

  • Published:
Rendiconti del Circolo Matematico di Palermo 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.

Bibliography

  1. J. Diaz,On an analogue of the Euler-Cauchy polygon method for the numerical solution of u xy =f(x, y, u, u x ,u y ), Arch. Rat. Mech. Anal.1 (1957), 154–180.

    Google Scholar 

  2. R. H. Moore,A Runge-Kutta procedure for the Goursat problem in hyperbolic partial differential equations, Arch. Rat. Mech. Anal. 7 (1961), 37–63.

    Article  MATH  Google Scholar 

  3. W. Törnig,Zur numerischen Behandlung von Anfangswertproblemen partieller hyperbolischer Differentialgleichungen zweiter Ordnung in zwei unabhängigen Veränderlichen, part I & II, Arch. Rat. Mech. Anal. 4 (1960), 428–466.

    Article  Google Scholar 

  4. P. Henrici,Discrete variable methods in ordinary differential equations, Wiley u. Sons, 1962.

  5. H. J. Stetter,Maximum bounds for the solutions of initial value problems for partial difference equations, Num. Math. 5 (1963), 399–424.

    Article  MATH  MathSciNet  Google Scholar 

  6. R. D. Richtmyer,Difference methods for initial value problems, Interscience Publ., 1957.

  7. H. J. Stetter,On the convergence of characteristic finite-difference methods of high accuracy for quasi-linear hyperbolic equations, Num. Math. 3 (1961), 321–344.

    Article  MATH  MathSciNet  Google Scholar 

  8. G. Dahlquist,Convergence and stability in the numerical integration of ordinary differential equations. Math. Scand. 4, 33–53 (1956).

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

During some phases of the preparation of this paper, the first author was supported in part by the AFOSR, European Office, under Grant No. AF-EOARDC 63-77; the paper was completed under the sponsorship of the Office of Naval Research, US Navy, while the first author was working at the University of California, Los Angeles (Numerical Analysis Research).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Steeter, H.J., Törnig, W. General multistep finite difference methods for the solution ofu xy =f(x, y, u, u x ,u y ). Rend. Circ. Mat. Palermo 12, 281–298 (1963). https://doi.org/10.1007/BF02851264

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02851264

Keywords

Navigation