
Splitting Schemes for NonStationary Problems with a Rational Approximation for Fractional Powers of the Operator
Problems of the numerical solution of the Cauchy problem for a firstord...
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Approximation of a fractional power of an elliptic operator
Some mathematical models of applied problems lead to the need of solving...
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Approximate representation of the solutions of fractional elliptical BVP through the solution of parabolic IVP
Boundary value problem for a fractional power of an elliptic operator is...
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A Survey on Numerical Methods for Spectral SpaceFractional Diffusion Problems
The survey is devoted to numerical solution of the fractional equation A...
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The Best Uniform Rational Approximation: Applications to Solving Equations Involving Fractional powers of Elliptic Operators
In this paper we consider one particular mathematical problem of this la...
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On the power of standard information for tractability for L_2approximation in the average case setting
We study multivariate approximation in the average case setting with the...
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Tensor Method for Optimal Control Problems Constrained by Fractional 3D Elliptic Operator with Variable Coefficients
We introduce the tensor numerical method for solving optimal control pro...
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Some methods for solving equations with an operator function and applications for problems with a fractional power of an operator
Several applied problems are characterized by the need to numerically solve equations with an operator function (matrix function). In particular, in the last decade, mathematical models with a fractional power of an elliptic operator and numerical methods for their study have been actively discussed. Computational algorithms for such nonstandard problems are based on approximations by the operator function. The most widespread are the approaches using various options for rational approximation. Also, we note the methods that relate to approximation by exponential sums. In this paper, the possibility of using approximation by exponential products is noted. The solution of an equation with an operator function is based on the transition to standard stationary or evolutionary problems. General approaches are illustrated by a problem with a fractional power of the operator. The first class of methods is based on the integral representation of the operator function under rational approximation, approximation by exponential sums, and approximation by exponential products. The second class of methods is associated with solving an auxiliary Cauchy problem for some evolutionary equation.
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