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BIT Numerical Mathematics

, Volume 57, Issue 4, pp 1153–1184 | Cite as

On singular BVPs with nonsmooth data: convergence of the collocation schemes

  • Jana Burkotová
  • Irena Rachůnková
  • Ewa B. Weinmüller
Article

Abstract

This paper deals with the collocation method applied to solve systems of singular linear ordinary differential equations with variable coefficient matrices and nonsmooth inhomogeneities. The classical stage convergence order is shown to hold for the piecewise polynomial collocation applied to boundary value problems with time singularities of the first kind provided that their solutions are appropriately smooth. The convergence theory is illustrated by numerical examples.

Keywords

Linear systems of ordinary differential equations Singular boundary value problems Time singularity of the first kind Nonsmooth inhomogeneity Collocation method Convergence 

Mathematics Subject Classification

65L05 65L10 65L20 65L60 

Notes

Acknowledgements

We wish to thank M.Sc. Michael Hubner and M.Sc. Stefan Wurm, Vienna University of Technology, for the numerical simulations.

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Copyright information

© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  • Jana Burkotová
    • 1
  • Irena Rachůnková
    • 1
  • Ewa B. Weinmüller
    • 2
  1. 1.Department of Mathematical Analysis and Applications of Mathematics, Faculty of SciencePalacký University OlomoucOlomoucCzech Republic
  2. 2.Department for Analysis and Scientific ComputingVienna University of TechnologyWienAustria

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