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Approximating a Retarded-Advanced Differential Equation Using Radial Basis Functions

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Computational Science and Its Applications – ICCSA 2017 (ICCSA 2017)

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Abstract

In last years we have got the approximation of the solution of a linear mixed type functional differential equation, considering the autonomous and non-autonomous case by collocation, least squares and finite element methods considering a polynomial basis. The present work introduces a numerical scheme using collocation and radial basis functions to solve numerically the non-linear mixed type equation with symmetric delay and advance. The results are similar using collocation, B-splines and exponential radial functions. The preliminary results are promising, but more simulations using different basis of radial functions are needed.

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Acknowledgements

This work was supported by Portuguese funds through the Center for Computational and Stochastic Mathematics (CEMAT), The Portuguese Foundation for Science and Technology (FCT), University of Lisbon, Portugal, project UID/Multi-/04621/2013, and Center of Naval Research (CINAV), Naval Academy, Portuguese Navy, Portugal.

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Authors and Affiliations

  1. CEMAT, Instituto Superior Técnico, Lisbon University, Av. Rovisco Pais, 1, 1048-001, Lisbon, Portugal

    M. Filomena Teodoro

  2. CINAV, Naval Academy, Base Naval de Lisboa, Alfeite, 1910-001, Almada, Portugal

    M. Filomena Teodoro

Authors
  1. M. Filomena Teodoro
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Correspondence to M. Filomena Teodoro .

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Editors and Affiliations

  1. University of Perugia, Perugia, Italy

    Osvaldo Gervasi

  2. University of Basilicata, Potenza, Italy

    Beniamino Murgante

  3. Covenant University, Ota, Nigeria

    Sanjay Misra

  4. University of Trieste, Trieste, Italy

    Giuseppe Borruso

  5. Polytechnic University of Bari, Bari, Italy

    Carmelo M. Torre

  6. University of Minho, Braga, Portugal

    Ana Maria A.C. Rocha

  7. Monash University, Clayton, Victoria, Australia

    David Taniar

  8. Kyushu Sangyo University, Fukuoka, Japan

    Bernady O. Apduhan

  9. Saint Petersburg State University, Saint Petersburg, Russia

    Elena Stankova

  10. University of Trieste, Trieste, Italy

    Alfredo Cuzzocrea

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Teodoro, M.F. (2017). Approximating a Retarded-Advanced Differential Equation Using Radial Basis Functions. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2017. ICCSA 2017. Lecture Notes in Computer Science(), vol 10408. Springer, Cham. https://doi.org/10.1007/978-3-319-62404-4_3

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  • DOI: https://doi.org/10.1007/978-3-319-62404-4_3

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