https://doi.org/10.1140/epjs/s11734-024-01416-8
Regular Article
Local meshless methods for elliptic PDEs with multipoint boundary conditions: investigating efficiency and accuracy of various RBFs
1
Department of Basic Sciences, University of Engineering and Technology Peshawar, Peshawar, Pakistan
2
Mathematics in Applied Sciences and Engineering Research Group, Scientific Research Center, Al-Ayen University, 64001, Nasiriyah, Iraq
3
Institute of Informatics and Computing in Energy (IICE), Universiti Tenaga Nasional, Kajang
, Selangor, Malaysia
b
mnawaz77@gmail.com
c
imtiazkakakhil@gmail.com
Received:
2
May
2024
Accepted:
14
November
2024
Published online:
28
November
2024
The present study addresses the numerical solution of two-dimensional steady-state heat conduction problems with nonlocal multi-point boundary conditions across three distinct domains: a unit rectangle with a quarter-circle cutout of radius 0.5, an irregular domain, and a Cassini curve. Dirichlet boundary conditions are imposed on specific segments, while nonlocal boundary conditions are applied to the remaining portions. The Kansa method is employed to solve the steady-state heat conduction equation, utilizing three types of radial basis functions (RBFs) to explore the influence of the shape parameter on accuracy and matrix conditioning. These include the inverse multiquadric RBF, a modified inverse multiquadric RBF proposed here for the first time, and a hybrid RBF [1]. As a meshless method, the Kansa approach eliminates the need for mesh generation or node connectivity within local subdomains. To evaluate accuracy and performance, the 
error norm is employed. The results demonstrate the effectiveness of the proposed techniques in solving the 2D steady-state heat conduction problem. A comparative analysis is conducted to assess the accuracy and computational efficiency of the methods.
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