Approximate representation of the solutions of fractional elliptical BVP through the solution of parabolic IVP
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Boundary value problem for a fractional power of an elliptic operator is considered. An integral representation by means of a standard solution problem for parabolic equations is used to solve such problems. Quadrature generalized Gauss-Laguerre formulas are constructed. We examine the effect of key parameters on the accuracy of the approximate solution: the number of nodes of the quadrature and fractional power of the operator. Computational experiments were performed to model two-dimensional problem with a fractional power of an elliptic operator.
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