Meshless Analysis of Nonlocal Boundary Value Problems in Anisotropic and Inhomogeneous Media

Zaheer-ud-Din, Muhammad Ahsan, Masood Ahmad, Wajid Khan, Emad E. Mahmoud and Abdel-Haleem Abdel-Aty
Additional contact information
Zaheer-ud-Din: Department of Basic Sciences, CECOS University of IT and Emerging Sciences Peshawar, Peshawar 25000, Pakistan
Muhammad Ahsan: Department of Basic Sciences, University of Engineering and Technology Peshawar, Peshawar 25000, Pakistan
Masood Ahmad: Department of Basic Sciences, University of Engineering and Technology Peshawar, Peshawar 25000, Pakistan
Wajid Khan: Department of Basic Sciences, University of Engineering and Technology Peshawar, Peshawar 25000, Pakistan
Emad E. Mahmoud: Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia
Abdel-Haleem Abdel-Aty: Department of Physics, College of Sciences, University of Bisha, P.O. Box 344, Bisha 61922, Saudi Arabia

Mathematics, 2020, vol. 8, issue 11, 1-19

Abstract: In this work, meshless methods based on a radial basis function (RBF) are applied for the solution of two-dimensional steady-state heat conduction problems with nonlocal multi-point boundary conditions (NMBC). These meshless procedures are based on the multiquadric (MQ) RBF and its modified version (i.e., integrated MQ RBF). The meshless method is extended to the NMBC and compared with the standard collocation method (i.e., Kansa’s method). In extended methods, the interior and the boundary solutions are approximated with a sum of RBF series, while in Kansa’s method, a single series of RBF is considered. Three different sorts of solution domains are considered in which Dirichlet or Neumann boundary conditions are specified on some part of the boundary while the unknown function values of the remaining portion of the boundary are related to a discrete set of interior points. The influences of NMBC on the accuracy and condition number of the system matrix associated with the proposed methods are investigated. The sensitivity of the shape parameter is also analyzed in the proposed methods. The performance of the proposed approaches in terms of accuracy and efficiency is confirmed on the benchmark problems.

Keywords: meshless method; integrated MQ RBF; steady-state heat conduction equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.mdpi.com/2227-7390/8/11/2045/pdf (application/pdf)
https://www.mdpi.com/2227-7390/8/11/2045/ (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:8:y:2020:i:11:p:2045-:d:446225

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 ().