Numerische Mathematik

, Volume 58, Issue 1, pp 855–873

Stability of a spline collocation method for strongly elliptic multidimensional singular integral equations

  • R. Schneider

DOI: 10.1007/BF01385658

Cite this article as:
Schneider, R. Numer. Math. (1990) 58: 855. doi:10.1007/BF01385658


We consider a spline collocation method for strongly elliptic zero order pseudodifferential equationspgwAu=f on a cube ω=(0, 1)m. Utilizing multilinear spline functions which are zero at the boundary σω we collocate at the meshpoints inside ω. For classical strongly elliptic translation invariant pseudodifferential operators, we verify the stability of the considered collocation method inL2(ω). Afterwards, form≦2 and a right hand sidefH8(ω),s>m/2, we prove an asymptotic convergence estimate.

Subject classifications

AMS(MOS): 45L10 45P05 47G05 47G05 65N30 65N99 65R20 73K30 CR: G.1.9 

Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • R. Schneider
    • 1
  1. 1.Fachbereich MathematikTechnische Hochschule DarmstadtDarmstadtGermany

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