Skip to main content
SpringerLink
Log in

Solution of bi-linear systems arising from high order discretizations of poisson-type equations

  • Part II Numerical Mathematics
  • Published:
BIT Numerical Mathematics Aims and scope Submit manuscript

Abstract

Bi-linear systems of the formAV+WA=G are obtained by approximating Poisson-type equations using higher-order finite difference formulae whereV,W andG are known matrices. Solution of the bi-linear system requiresO(n 3) operations for ann×n mesh. However, due to the increased accuracy obtained when using a high-order discretization formula,n can be made much smaller than in the conventional methods and indicates that faster Poisson-solvers which are numerically stable can be obtained by considering the bilinear system rather than the composite matrix form.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. R. E. Bank and D. J. Rose,Marching algorithms for elliptic boundary value problems, I:The constant coefficient case, SIAM J. Numer. Anal., 14 (1977), 792–829.

    Article  Google Scholar 

  2. W. G. Bickley and J. McNamee,Matrix and other direct methods for the solution of systems of linear difference equations, Philos. Trans. Roy. Soc. London Ser. A, 252 (1960), 69–131.

    Google Scholar 

  3. B. L. Buzbee, G. H. Golub and C. W. Nielson,On direct methods for solving Poisson's equations, SIAM J. Numer. Anal., 7 (1970), 627–656.

    Article  Google Scholar 

  4. R. Courant and D. Hilbert,Methods of Mathematical Physics, Vol. 2, Interscience, New York, 1966.

    Google Scholar 

  5. W. D. Hoskins, D. S. Meek and D. J. Walton,The numerical solution of the matrix equation X A+AY=F, BIT 17 (1977), 184–190.

    Google Scholar 

  6. G. M. Pathan,Higher order discretizations of elliptic partial differential equations, M.Sc. thesis, Lakehead University, Canada, 1979.

    Google Scholar 

  7. P. N. Swartztrauber,A direct method for the discrete solution of separable elliptic equations, SIAM J. Numer. Anal., 11 (1974), 1136–1150.

    Article  Google Scholar 

  8. R. A. Sweet,A cyclic reduction algorithm for solving block tridiagonal systems of arbitrary dimension, SIAM J. Numer. Anal., 14 (1977), 706–720.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, University of Manitoba, R3T 2N2, Winnipeg, Canada

    W. D. Hoskins, G. M. Pathan & D. J. Walton

  2. Department of Mathematical Sciences, Lakehead University, P7B 5E1, Thunder Bay, Canada

    W. D. Hoskins, G. M. Pathan & D. J. Walton

Authors
  1. W. D. Hoskins
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. M. Pathan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. D. J. Walton
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hoskins, W.D., Pathan, G.M. & Walton, D.J. Solution of bi-linear systems arising from high order discretizations of poisson-type equations. BIT 20, 212–214 (1980). https://doi.org/10.1007/BF01933193

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01933193

Keywords

Search

Navigation