COMBINED METHOD OF SEPARATION OF VARIABLES. 1. CRITICAL ANALYSIS OF THE KNOWN APPROACH

For the purpose of development of a new high-accuracy method of separation of variables, allowing one to effectively use the method of differential transformations in combination with the method of weighted residuals, by the example of the problems on the nonstationary heat conduction of an unbounded plate, an unbounded cylinder, and a sphere with the fi rst-kind boundary conditions, a critical analysis of the known solution technique based on the combined use of the Fourier method of separation of variables, the method of differential transformations, and the method of weighted residuals has been performed. It is shown that the computational scheme realized with the indicated technique has a very low approximation accuracy, especially in the case where it is used for bodies of cylindrical and spherical symmetry. The main reasons for the low accuracy of the solutions obtained by this scheme were revealed.
   
Author:  V. A. Kot
Keywords:  heat conduction equation, boundary-value problem, method of separation of variables, weighted residual method, eigenvalues, eigenfunctions, method of differential transformations
Page:  944