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

Samaneh Mokhtari, Ali Mesforush (), Reza Mokhtari, Rahman Akbari and Clemens Heitzinger
Additional contact information
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

Mathematics, 2023, vol. 11, issue 9, 1-13

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.

Keywords: stochastic non-linear Poisson–Boltzmann equation; biomolecular modeling; collocation method; radial basis functions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/9/2118/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/9/2118/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:9:p:2118-:d:1136846

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().