Construction and use of numerical-analytical approximating functions

11th International Conference on "Mesh methods for boundary-value problems and applications"

Serazutdinov, M.N.^1

Kazan National Research Technological University, 68 Karl Marx street, Kazan

420015, Russia^1

关键词: Analytical functions;    Different shapes;    Fourth order;    Higher derivatives;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/158/1/012082/pdf
DOI  :  10.1088/1757-899X/158/1/012082

来源: IOP

【 摘 要 】

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.