IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i9p2118-d1136846.html
   My bibliography  Save this article

Solving Stochastic Nonlinear Poisson-Boltzmann Equations Using a Collocation Method Based on RBFs

Author

Listed:
  • Samaneh Mokhtari

    (Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood 36199-95161, Iran)

  • Ali Mesforush

    (Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood 36199-95161, Iran)

  • Reza Mokhtari

    (Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-83111, Iran)

  • Rahman Akbari

    (Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-83111, Iran)

  • Clemens Heitzinger

    (Institute of Analysis and Scientific Computing, TU Wien, 1040 Vienna, Austria)

Abstract

In this paper, we present a numerical scheme based on a collocation method to solve stochastic non-linear Poisson–Boltzmann equations (PBE). This equation is a generalized version of the non-linear Poisson–Boltzmann equations arising from a form of biomolecular modeling to the stochastic case. Applying the collocation method based on radial basis functions (RBFs) allows us to deal with the difficulties arising from the complexity of the domain. To indicate the accuracy of the RBF method, we present numerical results for two-dimensional models, we also study the stability of this method numerically. We examine our results with the RBF-reference value and the Chebyshev Spectral Collocation (CSC) method. Furthermore, we discuss finding the appropriate shape parameter to obtain an accurate numerical solution besides greatest stability. We have exerted the Newton–Raphson approach for solving the system of non-linear equations resulting from discretization by the RBF technique.

Suggested Citation

  • Samaneh Mokhtari & Ali Mesforush & Reza Mokhtari & Rahman Akbari & Clemens Heitzinger, 2023. "Solving Stochastic Nonlinear Poisson-Boltzmann Equations Using a Collocation Method Based on RBFs," Mathematics, MDPI, vol. 11(9), pages 1-13, April.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:9:p:2118-:d:1136846
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/9/2118/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/9/2118/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. R. Cavoretto & A. Rossi & M. S. Mukhametzhanov & Ya. D. Sergeyev, 2021. "On the search of the shape parameter in radial basis functions using univariate global optimization methods," Journal of Global Optimization, Springer, vol. 79(2), pages 305-327, February.
    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. Zheng, Sanpeng & Feng, Renzhong, 2023. "A variable projection method for the general radial basis function neural network," Applied Mathematics and Computation, Elsevier, vol. 451(C).
    2. Petr Fedoseev & Artur Karimov & Vincent Legat & Denis Butusov, 2022. "Preference and Stability Regions for Semi-Implicit Composition Schemes," Mathematics, MDPI, vol. 10(22), pages 1-13, November.
    3. Li, Yang & Liu, Dejun & Yin, Zhexu & Chen, Yun & Meng, Jin, 2023. "Adaptive selection strategy of shape parameters for LRBF for solving partial differential equations," Applied Mathematics and Computation, Elsevier, vol. 440(C).
    4. Chen, Chuin-Shan & Noorizadegan, Amir & Young, D.L. & Chen, C.S., 2023. "On the selection of a better radial basis function and its shape parameter in interpolation problems," Applied Mathematics and Computation, Elsevier, vol. 442(C).
    5. Martín Alejandro Valencia-Ponce & Esteban Tlelo-Cuautle & Luis Gerardo de la Fraga, 2021. "Estimating the Highest Time-Step in Numerical Methods to Enhance the Optimization of Chaotic Oscillators," Mathematics, MDPI, vol. 9(16), pages 1-15, August.

    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:11:y:2023:i:9:p:2118-:d:1136846. 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.