Approximate representation of the solutions of fractional elliptical BVP through the solution of parabolic IVP

Abstract

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.