COMBINED METHOD OF SEPARATION OF VARIABLES. 2. SEQUENCES OF DIFFERENTIAL RELATIONS: PLATE, CYLINDER, SPHERE

By the example of the Sturm–Liouville problem, solved for the function V(y) determined in the region Ωy ∈ [0, 1] and corresponding to problems on the nonstationary heat conduction of a lengthy plate, a lengthy cylinder, and a sphere with symmetric boundary conditions of the fi rst, second, and third kind, the existence of infi nite sequences of differential relations at the boundary points y = 0 and y = 1 has been established. It is shown that these sequences of differential relations can be used to advantage in approximately solving the Sturm–Liouville problem for the function V(y) defi ned by a power polynomial with coeffi cients determined from the solution of the corresponding systems of linear algebraic equations.
   
Author:  V. A. Kot
Keywords:  heat conduction equation, boundary-value problem, method of separation of variables, differential relations.
Page:  1498