Title: Adaptative strategies for solving partial differential equations by Kansa's method

Authors: Selma Bouzit

Addresses: Faculty of Mathematics and Informatics, Mathematical Analysis and Applications Laboratory, Department of Mathematics, Mohamed El Bachir El Ibrahimi University of Bordj Bou Arreridj, El Anasser, 34030, Algeria

Abstract: This work presents an innovative and efficient meshless method for solving high-dimensional partial differential equations (PDEs). By utilising generalised multiquadric radial basis functions (GMQRBF) with an exponent β, the method incorporates various shape parameter c selection strategies to enhance numerical accuracy. Three approaches: optimal, trigonometric, and random for β and c are analysed for their performance across different problems. The method's mathematical foundation is rigorously studied, and extensive numerical experiments confirm its accuracy and robustness in solving linear and nonlinear PDEs across various dimensions. The results demonstrate its potential as a reliable and versatile tool for high-dimensional PDE applications.

Keywords: PDEs; partial differential equations; linear problems; non-linear problems; RBFs; radial basis functions; Kansa method; shape parameter.

DOI: 10.1504/IJCSM.2025.151300

International Journal of Computing Science and Mathematics, 2025 Vol.22 No.4, pp.311 - 321

Accepted: 20 May 2025
Published online: 22 Jan 2026 *

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