BIT Numerical Mathematics

, Volume 25, Issue 4, pp 652–666 | Cite as

B-convergence of the implicit midpoint rule and the trapezoidal rule

  • J. F. B. M. Kraaijevanger
Part II Numerical Mathematics


We present upper bounds for the global discretization error of the implicit midpoint rule and the trapezoidal rule for the case of arbitrary variable stepsizes. Specializing our results for the case of constant stepsizes they easily prove second order optimal B-convergence for both methods.

1980 AMS Subject Classification: 65L05, 65L20.

Keywords and Phrases

Numerical analysis stiff initial value problems implicit midpoint rule trapezoidal rule convergence variable stepsizes 


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Copyright information

© BIT Foundations 1985

Authors and Affiliations

  • J. F. B. M. Kraaijevanger
    • 1
  1. 1.Institute of Applied Mathematics and Computer ScienceUniversity of LeidenLeidenThe Netherlands

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