Sensitivity of Differential Equations

  • R. V. M. Zahar
Part of the Software Science and Engineering book series (SSEN)


Although it had received little attention until recently, the sensitivity of two-point boundary value problems in differential equations is the subject of much current study (see, for instance Reference 1). The question of how the solution of a differential system depends on its data is not only fundamental in analyzing differential models for physical processes, but it is essential for understanding numerical methods for solving the system. Indeed the sensitivity of the difference systems that approximate differential systems must depend in one way or another on the sensitivity of the original problem. Thus it is mathematically convenient to present a conditioning analysis that applies to both the differential and the difference systems. Chapter 11 develops the basis for such a uniform analysis.


Differential System Amplification Factor Fundamental Matrix Conditioning Analysis Linear Differential System 
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    Lentini, M.; Osborne, M. R. ;and Russell, R. D. “The close relationships between methods for solving two-point boundary value problems.” SIAM J. Numer. Anal. 22, 280–309 (1985).MathSciNetMATHCrossRefGoogle Scholar
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    Ince, E. L. Ordinary Differential Equations. Dover, London 1926.408.Google Scholar
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    Gautschi, W. Zur Numerik rekurrenter Relationen Computing 9, 107–26 (1972).MathSciNetMATHCrossRefGoogle Scholar
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    Jalbert, F.; and Zahar, R. V. M. “A highly precise Taylor series method for stiff O.D.E.s.” Cong. Numer. 46, 347–58 (1985).MathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • R. V. M. Zahar
    • 1
  1. 1.University of MontrealCanada

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