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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2024 MCQ for Mathematics of Computation is 1.78.

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An example of ill-conditioning in the numerical solution of singular perturbation problems
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by Fred W. Dorr PDF
Math. Comp. 25 (1971), 271-283 Request permission

Abstract:

The use of finite-difference methods is considered for solving a singular perturbation problem for a linear ordinary differential equation with an interior turning point. Computational results demonstrate that such problems can lead to very ill-conditioned matrix equations.
References
    I. Babuška, Numerical Stability in the Solution of the Tri-Diagonal Matrices, Report BN-609, The Institute for Fluid Dynamics and Applied Mathematics, University of Maryland, College Park, Md., 1969. I. Babuška, Numerical Stability in Problems in Linear Algebra, Report BN-663, The Institute for Fluid Dynamics and Applied Mathematics, University of Maryland, College Park, Md., 1970. F. W. Dorr, The Asymptotic Behavior and Numerical Solution of Singular Perturbation Problems with Turning Points, Ph.D. Thesis, University of Wisconsin, Madison, Wis., 1969.
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Additional Information
  • © Copyright 1971 American Mathematical Society
  • Journal: Math. Comp. 25 (1971), 271-283
  • MSC: Primary 65L05
  • DOI: https://doi.org/10.1090/S0025-5718-1971-0297142-0
  • MathSciNet review: 0297142