Journal
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
Volume 318, Issue -, Pages 378-387Publisher
ELSEVIER
DOI: 10.1016/j.cam.2016.07.025
Keywords
Meshless methods; Generalized finite difference method; Non-linear elliptic partial differential equations; Newton-Raphson method
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Funding
- Escuela Tecnica Superior de Ingenieros Industriales (UNED) of Spain [2016-IFC02]
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The generalized finite difference method (GFDM) has been proved to be a good meshless method to solve several linear partial differential equations (pde's): wave propagation, advection-diffusion, plates, beams, etc. The GFDM allows us to use irregular clouds of nodes that can be of interest for modelling non-linear elliptic pde's. This paper illustrates that the GFD explicit formulae developed to obtain the different derivatives of the pde's are based on the existence of a positive definite matrix that it is obtained using moving least squares approximation and Taylor series development. Also it is shown that in 2D a regular neighbourhood of eight nodes can be regarded as a generalization of a classical finite difference formula with a sixth order truncation error. This paper shows the application of the GFDM to solving different non-linear problems including applications to heat transfer, acoustics and problems of mass transfer. (C) 2016 Elsevier B.V. All rights reserved.
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