Approximation of functions and their derivatives: A neural network implementation with applications

Autor:	Thanh Tran-Cong, T. Nguyen-Thien
Rok vydání:	1999
Předmět:	Partial differential equation Muffin-tin approximation Function approximation Approximation error Modeling and Simulation Numerical analysis Modelling and Simulation Applied Mathematics Mathematical analysis Partial derivative Boundary element method Domain (mathematical analysis) Mathematics
Zdroj:	Applied Mathematical Modelling. 23(9):687-704
ISSN:	0307-904X
DOI:	10.1016/s0307-904x(99)00006-2
Popis:	This paper reports a neural network (NN) implementation for the numerical approximation of functions of several variables and their first and second order partial derivatives. This approach can result in improved numerical methods for solving partial differential equations by eliminating the need to discretise the volume of the analysis domain. Instead only an unstructured distribution of collocation points throughout the volume is needed. An NN approximation of relevant variables for the whole domain based on these data points is then achieved. Excellent test results are obtained. It is shown how the method of approximation can then be used as part of a boundary element method (BEM) for the analysis of viscoelastic flows. Planar Couette and Poiseuille flows are used as illustrative examples.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0e79870384a91eff930166ea3cb63e20 Zobrazit plný text záznamu Full Text from ScienceDirect