Method of solution of non-stationary problems of heat conduction

The results of the development of an approximate analytical method of the solution of the nonstationary
problems of the heat conduction are considered in the paper. The method is based
on the collective use of the method of separating of the variable and orthogonal methods of the
weighted residuals. The high accuracy of the eigenvalues obtained from the boundary problem
of Sturm-Liouville solution is noted. For example, finding the first 17th eigenvalues, the fist
four eigenvalues with the accuracy up to the 16th decimal concur with their exact values, and
the last one, the 17th, concurs with the accuracy up to the first decimal. The high accuracy of
the eigenvalues is explained by the fact that due to the given method of solving the differential
equation of the boundary problem of Sturm-Liouville satisfies accurately in the number of
points of the region that is equal to the number of the eigenvalues.

Sturm - Liouville problem, analytical solution, orthogonal methods, separation of variables, satisfying the equation, eigenvalues