BIT Numerical Mathematics

, Volume 28, Issue 3, pp 678–700 | Cite as

Error of Runge-Kutta methods for stiff problems studied via differential algebraic equations

  • E. Hairer
  • Ch. Lubich
  • M. Roche
Part III Numerical Mathematics


Runge-Kutta methods are studied when applied to stiff differential equations containing a small stiffness parameter ε. The coefficients in the expansion of the global error in powers of ε are the global errors of the Runge-Kutta method applied to a differential algebraic system. A study of these errors and of the remainder of the expansion yields sharp error bounds for the stiff problem. Numerical experiments confirm the results.

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© BIT Foundations 1988

Authors and Affiliations

  • E. Hairer
    • 1
  • Ch. Lubich
    • 1
  • M. Roche
    • 1
  1. 1.Dept. de mathématiquesUniversité de GenèveGenève 24Switzerland

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