IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v7y2019i9p853-d267568.html
   My bibliography  Save this article

Numerical Integral Transform Methods for Random Hyperbolic Models with a Finite Degree of Randomness

Author

Listed:
  • M. Consuelo Casabán

    (Instituto Universitario de Matemática Multidisciplinar, Building 8G, access C, 2nd floor, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain)

  • Rafael Company

    (Instituto Universitario de Matemática Multidisciplinar, Building 8G, access C, 2nd floor, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain)

  • Lucas Jódar

    (Instituto Universitario de Matemática Multidisciplinar, Building 8G, access C, 2nd floor, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain)

Abstract

This paper deals with the construction of numerical solutions of random hyperbolic models with a finite degree of randomness that make manageable the computation of its expectation and variance. The approach is based on the combination of the random Fourier transforms, the random Gaussian quadratures and the Monte Carlo method. The recovery of the solution of the original random partial differential problem throughout the inverse integral transform allows its numerical approximation using Gaussian quadratures involving the evaluation of the solution of the random ordinary differential problem at certain concrete values, which are approximated using Monte Carlo method. Numerical experiments illustrating the numerical convergence of the method are included.

Suggested Citation

  • M. Consuelo Casabán & Rafael Company & Lucas Jódar, 2019. "Numerical Integral Transform Methods for Random Hyperbolic Models with a Finite Degree of Randomness," Mathematics, MDPI, vol. 7(9), pages 1-21, September.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:9:p:853-:d:267568
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/7/9/853/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/7/9/853/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Iacus, Stefano Maria, 2001. "Statistical analysis of the inhomogeneous telegrapher's process," Statistics & Probability Letters, Elsevier, vol. 55(1), pages 83-88, November.
    2. Jacek Banasiak & Janusz R. Mika, 1998. "Singularly perturbed telegraph equations with applications in the random walk theory," International Journal of Stochastic Analysis, Hindawi, vol. 11, pages 1-20, January.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. De Gregorio, Alessandro & Iafrate, Francesco, 2021. "Telegraph random evolutions on a circle," Stochastic Processes and their Applications, Elsevier, vol. 141(C), pages 79-108.
    2. Hosseininia, M. & Heydari, M.H., 2019. "Meshfree moving least squares method for nonlinear variable-order time fractional 2D telegraph equation involving Mittag–Leffler non-singular kernel," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 389-399.
    3. De Gregorio, Alessandro, 2009. "Parametric estimation for planar random flights," Statistics & Probability Letters, Elsevier, vol. 79(20), pages 2193-2199, October.
    4. Vieira, N. & Ferreira, M. & Rodrigues, M.M., 2022. "Time-fractional telegraph equation with ψ-Hilfer derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    5. Nicole Bauerle & Igor Gilitschenski & Uwe D. Hanebeck, 2014. "Exact and Approximate Hidden Markov Chain Filters Based on Discrete Observations," Papers 1411.0849, arXiv.org, revised Dec 2014.
    6. Macci, Claudio, 2016. "Large deviations for some non-standard telegraph processes," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 119-127.
    7. De Gregorio, Alessandro & Macci, Claudio, 2012. "Large deviation principles for telegraph processes," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 1874-1882.
    8. Weam Alharbi & Sergei Petrovskii, 2018. "Critical Domain Problem for the Reaction–Telegraph Equation Model of Population Dynamics," Mathematics, MDPI, vol. 6(4), pages 1-15, April.
    9. Johan GB Beumee & Chris Cormack & Peyman Khorsand & Manish Patel, 2014. "Path Diffusion, Part I," Papers 1406.0077, arXiv.org.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:7:y:2019:i:9:p:853-:d:267568. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.