GENERALIZED INTERPOLATION HERMITE – BIRKHOFF POLYNOMIALS FOR ARBITRARY-ORDER PARTIAL DIFFERENTIAL OPERATORS
https://doi.org/10.29235/1561-2430-2018-54-2-149-163
Abstract
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.
About the Authors
M. V. Ignatenko
Belarusian State University.
Belarus
Belarus
Marina V. Ignatenko –Ph.D. (PhysicsandMathematics), Associate Professor, Associate Professor of Web Technologies and Computer Simulation Department.
4, Nezavisimosti Ave., 220030, Minsk.
L. A. Yanovich
Institute of Mathematics of the National Aca demy of Sciences of Belarus.
Belarus
Belarus
Leonid A. Yanovich – Corresponding Member, D. Sc. (Physics and Mathematics), Professor, Chief Researcher.
11, Surganov Str., 220072, Minsk.
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