Two novel meshless methods for solving general fourth-order PDEs in irregular domains: Applications to plate bending problems

Xubo Lin, Sergiy Reutskiy, Ji Lin and Jun Lu

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 248, issue C, 794-823

Abstract: This paper presents two RBF-based meshless techniques for solving the fourth-order elliptic partial differential equations (PDEs) in complex geometries. The first method assumes splitting the given equation into a system of two Poisson ones. The second technique directly solves the given PDE of the fourth order if the splitting method does not work. The unifying idea of the both techniques is that the two problems (1) approximation of BC and (2) satisfaction of the governing PDE inside the solution domain are considered separately. Besides, the both techniques utilize series of the so-called modified RBFs (MRBFs) for approximation of the solution inside the solution domain. The direct approach yields a significantly higher accuracy and can be applied to a wide class of plate bending problems. The efficacy of the proposed methodologies is validated by illustrative test cases with different configuration and boundary conditions.

Keywords: Fourth-order equation; Numerical solution; Meshless method; Radial basis functions; Split technique (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:248:y:2026:i:c:p:794-823

DOI: 10.1016/j.matcom.2026.04.029

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