Numerische Mathematik

, Volume 41, Issue 2, pp 165–175 | Cite as

Smoothing the extrapolated midpoint rule

  • Lawrence F. Shampine
  • Lorraine S. Baca
The Uniform Stability of Singularly Perturbed Discrete and Continuous Boundary Value Problems


The extrapolated midpoint rule is a popular way to solve the initial value problem for a system of ordinary differential equations. As originally formulated by Gragg, the results are smoothed to remove the weak instability of the midpoint rule. It is shown that this smoothing is not necessary. A cheaper smoothing scheme is proposed. A way to exploit smoothing to increase the robustness of extrapolation codes is formulated.

Subject Classifications

AMS(MOS): 65LO5 CR: 5.17 


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Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • Lawrence F. Shampine
    • 1
  • Lorraine S. Baca
    • 1
  1. 1.Numerical Mathematics DivisionSandia National LaboratoriesAlbuquerqueUSA

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