Numerische Mathematik

, Volume 58, Issue 1, pp 369–386 | Cite as

Gaussian collocation via defect correction

  • K. H. Schild


For the numerical integration of boundary value problems for first order ordinary differential systems, collocation on Gaussian points is known to provide a powerful method. In this paper we introduce a defect correction method for the iterative solution of such high order collocation equations. The method uses the trapezoidal scheme as the ‘basic discretization’ and an adapted form of the collocation equations for defect evaluation. The error analysis is based on estimates of the contractive power of the defect correction iteration. It is shown that the iteration producesO(h2), convergence rates for smooth starting vectors. A new result is that the iteration damps all kind of errors, so that it can also handle non-smooth starting vectors successfully.

Subject classifications

AMS(MOS): 65L10 CR:G1.7 


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Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • K. H. Schild
    • 1
  1. 1.Fachbereich MathematikPhilipps-Universität MarburgMarburgGermany

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