Method of Chebyshev-Laguerre polynomials in three-dimensional dynamical problem of thermoelasticity (Q2753478)

A new approach to solution of three-dimensional dynamical problems of thermoelasticity is proposed. Use of the Laplace or Fourier transform in time is completed by an expansion in Chebyshev-Laguerre polynomials. In particular, axisymmetric and radially-symmetrical dynamical problems for a spherical solid are solved. Advantages of the technique are uniformity of its application to solutions of different non-stationary problems of continuum mechanics whose study by the classical methods is too complicated, and reducing computational efforts in numerical calculations. For comparison, an analogous radially-symmetrical problem is solved using the Laplace integral transform. Numerical results for this problem are compared with those obtained by the finite element method.