Volume 12, no. 2Pages 5 - 24

Inverse Spectral Problems and Mathematical Models of Continuum Mechanics

G.A. Zakirova
The article contains results in the field of spectral problems for mathematical models with discrete semi-bounded operator. The theory is based on linear formulas for calculating the eigenvalues of a discrete operator. The main idea is to reduce spectral problem to the Fredholm integral equation of the first kind. A computationally efficient numerical method for solving inverse spectral problems is developed. The method is based on the Galerkin method for discrete semi-bounded operators. This method allows to reconstruct the coefficient functions of boundary value problems with a high accuracy. The results obtained in the article are applicable to the study of problems for differential operators of any order. The results of a numerical solution of the inverse spectral problem for a fourth-order perturbed differential operator are presented. We study some mathematical models of continuum mechanics based on spectral problems for a discrete semi-bounded operator.
Full text
inverse spectral problem; discrete operator; fourth order operator; self-adjoint operator; eigenvalues; eigenfunctions; ill-posed problems.
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