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Finite element solution of a linear mixed-type functional differential equation

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Abstract

This paper is devoted to the approximate solution of a linear first-order functional differential equation which involves delayed and advanced arguments. We seek a solution x, defined for t ∈ (0, k − 1],(k ∈ IN ), which takes given values on the intervals [ − 1, 0] and (k − 1, k]. Continuing the work started in previous articles on this subject, we introduce and analyse a computational algorithm based on the finite element method for the solution of this problem which is applicable both in the case of constant and variable coefficients. Numerical results are presented and compared with the results obtained by other methods.

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Authors and Affiliations

  1. CEMAT, Instituto Superior Técnico, UTL, Av. Rovisco Pais, 1049-001, Lisboa, Portugal

    Pedro Miguel Lima & M. Filomena Teodoro

  2. Dep. de Matemática, EST, Instituto Politécnico de Setúbal, Estefanilha, 2910-761, Setúbal, Portugal

    M. Filomena Teodoro

  3. Department of Mathematics, University of Chester, CH1 4BJ, Chester, UK

    Neville J. Ford & Patricia M. Lumb

Authors
  1. Pedro Miguel Lima
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  2. M. Filomena Teodoro
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  3. Neville J. Ford
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  4. Patricia M. Lumb
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Corresponding author

Correspondence to Pedro Miguel Lima.

Additional information

M. Filomena Teodoro acknowledges support from FCT, grant SFRH/BD/37528/2007.

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Lima, P.M., Teodoro, M.F., Ford, N.J. et al. Finite element solution of a linear mixed-type functional differential equation. Numer Algor 55, 301–320 (2010). https://doi.org/10.1007/s11075-010-9412-y

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  • DOI: https://doi.org/10.1007/s11075-010-9412-y

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