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On using radial basis functions in a “finite difference mode” with applications to elasticity problems. (English) Zbl 1063.74104
Summary: A way of using radial basis fucntions (RBF) as the basis for PDE’s solvers is presented, its essence being constructing approximate formulas for derivative discretizations based on RBF interpolants with local supports similar to stencils in finite difference methods. Numerical results for different types of elasticity equations showing reasonable accuracy and good \(h\)-convergence properties of the technique are presented. In particular, examples of RBF solution in the case of non-linear Kármán-Foppl equation are considered.

MSC:
74S20 Finite difference methods applied to problems in solid mechanics
74B05 Classical linear elasticity
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