Skip to main content
SpringerLink
Log in

On the efficiency of a class of a-stable methods

  • Published:
BIT Numerical Mathematics Aims and scope Submit manuscript

Abstract

The numerical solution of systems of differential equations of the formB dx/dt=σ(t)Ax(t)+f(t),x(0) given, whereB andA (withB and —(A+A T) positive definite) are supposed to be large sparse matrices, is considered.A-stable methods like the Implicit Runge-Kutta methods based on Radau quadrature are combined with iterative methods for the solution of the algebraic systems of equations.

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. S. Varga,Functional analysis and approximation theory in numerical analysis, SIAM Publications, Philadelphia, 1971.

    Google Scholar 

  2. O. Widlund,A note on unconditionally stable linear multi-step methods, BIT 7 (1967), 65–70.

    Google Scholar 

  3. C. W. Gear,Numerical initial value problems in ordinary differential equations, Prentice-Hall, N.J., 1971.

  4. J. D. Lambert,Computational methods in ordinary differential equations, John Wiley, N.Y., 1973.

    Google Scholar 

  5. O. Axelsson,A class of A-stable methods, BIT 9 (1969), 185–199.

    Google Scholar 

  6. O. Axelsson,On the efficiency of some A-stable methods, Report DD/73/32, CERN, Geneva, Switzerland; 1973.

    Google Scholar 

  7. O. Axelsson,On preconditioning and convergence acceleration in sparse matrix problems, Report 73-16, Department of Computer Sciences, Chalmers University of Technology, Göteborg, Sweden; 1973.

    Google Scholar 

  8. A. H. Stroud and D. Secrest,Gaussian quadrature formulas, Prentice Hall, N.J., 1966.

    Google Scholar 

  9. J. L. Blue and H. K. Gummel,Rational approximations to matrix exponential for systems of stiff differential equations, J. Comput. Physics 5 (1970), 70–83.

    Article  Google Scholar 

  10. I. Fried,Optimal gradient minimization scheme for finite element eigenproblems, J. Sound Vibration 20 (1972), 333–342.

    Article  Google Scholar 

  11. J. A. George,Computer implementation of the finite element method, STAN-CS-71-208, Stanford University, 1971.

  12. A. J. Hoffman, M. S. Martin and D. J. Rose,Complexity bounds for regular finite difference and finite element grids, SIAM J. Numer. Anal. 10 (1973), 364–369.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Cern, Geneva, Switzerland

    O. Axelsson

Authors
  1. O. Axelsson
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

On leave from Chalmers University of Technology, Göteborg, Sweden.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Axelsson, O. On the efficiency of a class of a-stable methods. BIT 14, 279–287 (1974). https://doi.org/10.1007/BF01933227

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01933227

Keywords

Search

Navigation