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On nonlinear analysis by the multipoint meshless FDM. (English) Zbl 1403.65112
Summary: The main objective of this paper is to present an attempt of an application of the recently developed higher order multipoint meshless FDM in the analysis of nonlinear problems. The multipoint approach provides a higher order approximation and improves the precision of the solution. In addition to improved solution quality, the essential feature of the multipoint approach is its potentially wide ranging applicability. This is possible, because in both the multipoint and standard meshless FDM, the difference formulas are generated at once for the full set of derivatives. Using them, we may easily compose any required FD operator. It is worth mentioning that all derivative operators depend on the domain discretization rather than on the specific problem being analysed. Therefore, the solution of a wide class of problems including nonlinear ones, may be obtained with this method. The numerical algorithm of the multipoint method for nonlinear analysis is presented in this paper. Results of selected engineering benchmark problems – deflection of the ideal membrane and analysis of large deflection of plates using the von Karman theory – are considered.

MSC:
 65N06 Finite difference methods for boundary value problems involving PDEs 65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
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