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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 2020 MCQ for Mathematics of Computation is 1.78.

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.

 

Stability of sequences generated by nonlinear differential systems
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by R. Leonard Brown PDF
Math. Comp. 33 (1979), 637-645 Request permission

Abstract:

A local stability analysis is given for both the analytic and numerical solutions of the initial value problem for a system of ordinary differential equations. The standard linear stability analysis is reviewed, then it is shown that, using a proper choice of Liapunov function, a connected region of stable initial values of both the analytic solution and of the one-leg k-step numerical solution can be approximated computationally. Correspondence between the one-leg k-step solution and its associated linear k-step solution is shown, and two examples are given.
References
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    • G. DAHLQUIST, On Stability and Error Analysis for Stiff Non-Linear Problems, Report NA-7508, Dept. of Information Processing, Royal Institute of Technology, Stockholm, 1975. C. W. GEAR, "Algorithm 407: DIFSUB for solution of ordinary differential equations," Comm. ACM, v. 14, 1971, pp. 185-190.
  • C. William Gear, Numerical initial value problems in ordinary differential equations, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1971. MR 0315898
    • A. C. HINDMARSH, GEAR: Ordinary Differential Equation System Solver, UCID-300001, Rev. 2, Lawrence Livermore Lab., Livermore, California, 1972.
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    • W. LINIGER & F. ODEH, On Liapunov Stability of Stiff Non-Linear Multistep Difference Equations, AFOSR-TR-76-1023, IBM Thomas J. Watson Research Center, 1976.
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    • G. G. STEINMETZ, R. V. PARRISH & R. L. BOWLES, Longitudinal Stability and Control Derivatives of a Jet Fighter Airplane Extracted from Flight Test Data by Utilizing Maximum Likelihood Estimation, NASA-TV D-6532, NASA Langley Research Center, Hampton, Va., 1972. K. W. TU, Stability and Convergence of General Multistep and Multivalue Methods with Variable Stepsize, UIUCDCS-R-72-526, Univ. of Illinois, Urbana, Ill., 1972.
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Additional Information
  • © Copyright 1979 American Mathematical Society
  • Journal: Math. Comp. 33 (1979), 637-645
  • MSC: Primary 65L99; Secondary 34D20
  • DOI: https://doi.org/10.1090/S0025-5718-1979-0521279-9
  • MathSciNet review: 521279