Construction and use of numerical-analytical approximating functions

The article goes over the methodology of constructing numerical-analytical approximating functions, satisfying the given boundary conditions for the function of its derivatives in the circuit areas of various shapes. The methodology is based on presenting the unknown function as a series in a comple...

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Bibliographic Details
Published in:IOP conference series. Materials Science and Engineering 2016-11, Vol.158 (1), p.12082
Main Author: Serazutdinov, M N
Format: Article
Language:English
Subjects:
Approximation
Boundary conditions
Boundary value problems
Circuits
Contours
Derivatives
Finite difference method
Mathematical analysis
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Summary:The article goes over the methodology of constructing numerical-analytical approximating functions, satisfying the given boundary conditions for the function of its derivatives in the circuit areas of various shapes. The methodology is based on presenting the unknown function as a series in a complete set of functions that do not satisfy the given boundary conditions on the contour of the area, but additionally numerically defined near the contour to satisfy the boundary conditions. The additional definition of the functions near the area contour is performed numerically based on finite-difference relations. The main advantage of the stated method is the ability to build a relatively simple approximating functions satisfying the given boundary conditions on the boundary of complex shaped areas. The examples of applying the described method for solving the boundary value problem of a plate of different shapes. The possibility of using numerical-analytical functions for solving boundary value problems that contain higher derivatives up to fourth order is shown.
ISSN:1757-8981
1757-899X
DOI:10.1088/1757-899X/158/1/012082