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

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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.

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Notes

  1. For technical reasons the mesh is restricted to \(u_k<1\) and \(u_{k+1}:=1\).

  2. \(V=16.41619116478355\), \(D_0=0.00008333333333333334\), \(G_0=6.221834927724428\).

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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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Authors and Affiliations

  1. Department of Mathematical Analysis and Applications of Mathematics, Faculty of Science, Palacký University Olomouc, 17. listopadu 12, 77146, Olomouc, Czech Republic

    Jana Burkotová & Irena Rachůnková

  2. Department for Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstraße 8–10, 1040, Wien, Austria

    Ewa B. Weinmüller

Authors
  1. Jana Burkotová
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  2. Irena Rachůnková
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  3. Ewa B. Weinmüller
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Corresponding author

Correspondence to Jana Burkotová.

Additional information

Communicated by Ralf Hiptmair.

The first two authors gratefully acknowledge support received from the Grant No. 14-06958S of the Grant Agency of the Czech Republic.

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Burkotová, J., Rachůnková, I. & Weinmüller, E.B. On singular BVPs with nonsmooth data: convergence of the collocation schemes. Bit Numer Math 57, 1153–1184 (2017). https://doi.org/10.1007/s10543-017-0686-5

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