Hybrid local meshless method for solving elliptic boundary value problems

Document Type

Article

Publication Date

2-4-2025

Department

Mathematics

School

Mathematics and Natural Sciences

Abstract

We employ the method of particular solutions (MPS) for the numerical solution of two-dimensional Poisson and inhomogeneous biharmonic problems. An approximate particular solution is obtained using the local radial basis function (LRBF) method while the resulting homogeneous problems are solved using the local method of fundamental solutions (LMFS). Appropriate matrix decomposition algorithms may be employed in the construction of the approximate particular solution when the governing equation is extended and collocated in a radially symmetric region enclosing the physical domain of the problem in question. The results of several numerical experiments demonstrate the efficacy of the proposed approach.

Publication Title

Computational and Applied Mathematics

Volume

44

Issue

2

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