On a Class of Hermite Interpolation Polynomials for Nonlinear Second Order Partial Differential Operators
1 Institute of Mathematics, National Academy of Sciences of Belarus, Surganova Str. 11, 220072 Minsk, Belarus
2 Faculty of Mechanics and Mathematics, Belarus State University, Nezavisimosti Ave. 4, 220030 Minsk, Belarus
Published online: 14 February 2018
This article is devoted to the problem of construction of Hermite interpolation formulas with knots of the second multiplicity for second order partial differential operators given in the space of continuously differentiable functions of two variables. The obtained formulas contain the Gateaux differentials of a given operator. The construction of operator interpolation formulas is based on interpolation polynomials for scalar functions with respect to an arbitrary Chebyshev system of functions. An explicit representation of the interpolation error has been obtained.
© The Authors, published by EDP Sciences, 2018
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