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Quadrature Integration Techniques for Random Hyperbolic PDE Problems

Author

Listed:
  • Rafael Company

    (Instituto de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain)

  • Vera N. Egorova

    (Departamento de Matemática Aplicada y Ciencias de la Computación, Universidad de Cantabria, Avenida de los Castros s/n, 39005 Santander, Spain)

  • Lucas Jódar

    (Instituto de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain)

Abstract

In this paper, we consider random hyperbolic partial differential equation (PDE) problems following the mean square approach and Laplace transform technique. Randomness requires not only the computation of the approximating stochastic processes, but also its statistical moments. Hence, appropriate numerical methods should allow for the efficient computation of the expectation and variance. Here, we analyse different numerical methods around the inverse Laplace transform and its evaluation by using several integration techniques, including midpoint quadrature rule, Gauss–Laguerre quadrature and its extensions, and the Talbot algorithm. Simulations, numerical convergence, and computational process time with experiments are shown.

Suggested Citation

  • Rafael Company & Vera N. Egorova & Lucas Jódar, 2021. "Quadrature Integration Techniques for Random Hyperbolic PDE Problems," Mathematics, MDPI, vol. 9(2), pages 1-16, January.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:2:p:160-:d:480023
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    References listed on IDEAS

    as
    1. Joseph Abate & Ward Whitt, 2006. "A Unified Framework for Numerically Inverting Laplace Transforms," INFORMS Journal on Computing, INFORMS, vol. 18(4), pages 408-421, November.
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    Cited by:

    1. Lucas Jódar & Rafael Company, 2022. "Preface to “Mathematical Methods, Modelling and Applications”," Mathematics, MDPI, vol. 10(9), pages 1-2, May.

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