Информационная система "Конференции"

Abstracts

Numerical solution of differential and integral equations

When interpolating the univariate function on a compact set by use of a generalized polynomial the set of used basic functions must satisfy the following requirement. On that compact the number of points, where any generalized polynomial is zero, must be less than the number of its composant basic functions. Such compacts are named Chebyshevskian. J.C.,Mairhuber theorem concerning the Chebyshev approximation problem provides a solution uniqueness only for the case of one-dimensional compacts. In the multi-dimensional space $R^m$ every compact set having internal points certainly is not Chebyshev's one. The notion of the strong-linear independence for basic functions removes the above mentioned ban. Let $V$ be the set of continuously differentiable multivariate functions $v$ and of its partial derivatives such that every finite subset is strong linearly independent i.e. linearly independent on every dense set in any open full-sphere. Differentially conditioned generating is the constructing the linear combination $s(x)=sum limits_{k=1}^{K}d_{k},v_{k}, ;x in R^{m},$ which satisfy equations $L_{j}s=0$ in the given points $x_j,.$ Here every $L_j$ is a linear differential operator. In such a manner some forward and inverse problems for the partial differential equations can be set and solved because the level set $s(x)=0$ is nowhere dense in virtue of the strong-linear independence.

Note. Abstracts are published in author's edition

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