Skip to Main Content

Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.98.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

An example of ill-conditioning in the numerical solution of singular perturbation problems
HTML articles powered by AMS MathViewer

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.
  • Fred Dorr, The numerical solution of singular perturbations of boundary value problems, SIAM J. Numer. Anal. 7 (1970), 281–313. MR 267781, DOI 10.1137/0707021
  • F. W. Dorr and S. V. Parter, Singular perturbations of nonlinear boundary value problems with turning points, J. Math. Anal. Appl. 29 (1970), 273–293. MR 262622, DOI 10.1016/0022-247X(70)90079-X
  • F. W. Dorr & S. V. Parter, Extensions of Some Results on Singular Perturbation Problems With Turning Points, Report LA-4290-MS, Los Alamos Scientific Laboratory, Los Alamos, N. M., 1969. G. H. Golub, Matrix Decompositions and Statistical Calculations, Report CS-124, Computer Science Department, Stanford University, Stanford, Calif., 1969. D. Greenspan, Numerical Studies of Two Dimensional, Steady State Navier-Stokes Equations for Arbitrary Reynolds Number, Report 9, Computer Sciences Department, University of Wisconsin, Madison, Wis., 1967.
  • W. D. Murphy, Numerical analysis of boundary-layer problems in ordinary differential equations, Math. Comp. 21 (1967), 583–596. MR 225496, DOI 10.1090/S0025-5718-1967-0225496-9
  • B. Noble, Personal Communication, University of Wisconsin, Madison, Wis., Feb. 19, 1970.
  • Carl E. Pearson, On a differential equation of boundary layer type, J. Math. and Phys. 47 (1968), 134–154. MR 228189
  • Carl E. Pearson, On non-linear ordinary differential equations of boundary layer type, J. Math. and Phys. 47 (1968), 351–358. MR 237107
  • Harvey S. Price, Richard S. Varga, and Joseph E. Warren, Application of oscillation matrices to diffusion-convection equations, J. Math. and Phys. 45 (1966), 301–311. MR 207230
  • Harvey S. Price and Richard S. Varga, Error bounds for semidiscrete Galerkin approximations of parabolic problems with applications to petroleum reservoir mechanics, Numerical Solution of Field Problems in Continuum Physics (Proc. Sympos. Appl. Math., Durham, N.C., 1968) Amer. Math. Soc., Providence, R.I., 1970, pp. 74–94. MR 0266452
  • Richard S. Varga, Matrix iterative analysis, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1962. MR 0158502
  • J. H. Wilkinson, The algebraic eigenvalue problem, Clarendon Press, Oxford, 1965. MR 0184422
Similar Articles
  • Retrieve articles in Mathematics of Computation with MSC: 65L05
  • Retrieve articles in all journals with MSC: 65L05
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