Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

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

Version 1 : Received: 29 September 2020 / Approved: 30 September 2020 / Online: 30 September 2020 (14:31:00 CEST)

How to cite: Muhammad, Z.; Ahsan, M.; Ahmad, M.; Khan, W.; Mahmoud, E.E.; Abdel-Aty, A. Meshless Analysis of Nonlocal Boundary Value Problems in Anisotropic and Inhomogeneous Media. Preprints 2020, 2020090751 (doi: 10.20944/preprints202009.0751.v1). Muhammad, Z.; Ahsan, M.; Ahmad, M.; Khan, W.; Mahmoud, E.E.; Abdel-Aty, A. Meshless Analysis of Nonlocal Boundary Value Problems in Anisotropic and Inhomogeneous Media. Preprints 2020, 2020090751 (doi: 10.20944/preprints202009.0751.v1).

Abstract

In this work, meshless methods 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 multiquadric radial basis function (MQ RBF) and its modified version (i.e. integrated MQ RBF). The proposed meshless methods which were recently published in \cite{Reutskiy2016} is compared with standard collocation method (i.e. Kansa's method). Three different sorts of solution domain are considered in which Dirichlet boundary condition is specified on some part of the boundary and is related to the unknown function values at a discrete set of interior points. The influence of NMBC on the accuracy and condition number of the system matrix associated to the proposed methods is investigated. The sensitivity of the shape parameter is also analyzed in the proposed methods. Performance of the proposed approaches in terms of accuracy and efficiency is confirmed on the benchmark problems.

Subject Areas

Meshless method; Integrated MQ RBF; Steady-state heat conduction equation

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