An Economic Method for Evaluation of Volume Integrals

  • Natalia T. Kolkovska
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3401)


Approximations to the volume integrals with logarithmic kernels are obtained as solutions to finite difference schemes on the regular grid in a rectangular domain, which contains the domain of integration. Two types of right-hand sides in the finite difference equations are constructed – the first one includes some double and line integrals and the second one is fully discrete. The error estimates (optimal with respect to the smoothness of the volume integral) for both types of right-hand sides are obtained for volume integrals in appropriate Besov spaces.


volume integrals integral equations particular solution Poisson equation 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Natalia T. Kolkovska
    • 1
  1. 1.Institute of Mathematics and InformaticsBulgarian Academy of Sciences 

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