Open AccessGENERALIZED INTERPOLATION HERMITE – BIRKHOFF POLYNOMIALS FOR ARBITRARY-ORDER PARTIAL DIFFERENTIAL OPERATORS
Author(s) -
Марина Викторовна Игнатенко,
L. A. Yanovich
Publication year - 2018
Publication title -
vescì nacyânalʹnaj akadèmìì navuk belarusì. seryâ fìzìka-matèmatyčnyh navuk
Language(s) - English
Resource type - Journals
eISSN - 2524-2415
pISSN - 1561-2430
DOI - 10.29235/1561-2430-2018-54-2-149-163
Subject(s) - mathematics , birkhoff interpolation , hermite interpolation , trigonometric interpolation , interpolation (computer graphics) , hermite polynomials , differential operator , operator theory , operator (biology) , mathematical analysis , pure mathematics , algebra over a field , polynomial interpolation , linear interpolation , polynomial , computer science , animation , biochemistry , chemistry , computer graphics (images) , repressor , transcription factor , gene
This article is devoted to the problem of construction and research of the generalized Hermite – Birkhoff interpolation formulas for arbitrary-order partial differential operators given in the space of continuously differentiable functions of many variables. The construction of operator interpolation polynomials is based both on interpolation polynomials for scalar functions with respect to an arbitrary Chebyshev system, and on the generalized Hermite – Birkhoff interpolation formulas obtained earlier by the authors for general operators in functional spaces. The presented operator formulas contain the Stieltjes integrals and the Gateaux differentials of an interpolated operator. An explicit representation of the error of operator interpolation was obtained. Some special cases of the generalized Hermite – Birkhoff formulas for partial differential operators are considered. The obtained results can be used in theoretical research as the basis for constructing approximate methods for solution of some nonlinear operator-differential equations found in mathematical physics.